(x+5)/(25x^2-10x)+(x+4)/(20x^2+8x)=9/(25x^2-4)

Simple and best practice solution for (x+5)/(25x^2-10x)+(x+4)/(20x^2+8x)=9/(25x^2-4) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for (x+5)/(25x^2-10x)+(x+4)/(20x^2+8x)=9/(25x^2-4) equation:

D( x )

25*x^2-(10*x) = 0

25*x^2-4 = 0

20*x^2+8*x = 0

25*x^2-(10*x) = 0

25*x^2-(10*x) = 0

25*x^2-10*x = 0

25*x^2-10*x = 0

DELTA = (-10)^2-(0*4*25)

DELTA = 100

DELTA > 0

x = (100^(1/2)+10)/(2*25) or x = (10-100^(1/2))/(2*25)

x = 2/5 or x = 0

25*x^2-4 = 0

25*x^2-4 = 0

25*x^2 = 4 // : 25

x^2 = 4/25

x^2 = 4/25 // ^ 1/2

abs(x) = 2/5

x = 2/5 or x = -2/5

20*x^2+8*x = 0

20*x^2+8*x = 0

20*x^2+8*x = 0

DELTA = 8^2-(0*4*20)

DELTA = 64

DELTA > 0

x = (64^(1/2)-8)/(2*20) or x = (-64^(1/2)-8)/(2*20)

x = 0 or x = -2/5

x in (-oo:-2/5) U (-2/5:0) U (0:2/5) U (2/5:+oo)

(x+5)/(25*x^2-(10*x))+(x+4)/(20*x^2+8*x) = 9/(25*x^2-4) // - 9/(25*x^2-4)

(x+5)/(25*x^2-(10*x))+(x+4)/(20*x^2+8*x)-(9/(25*x^2-4)) = 0

(x+5)/(25*x^2-10*x)+(x+4)/(20*x^2+8*x)-9*(25*x^2-4)^-1 = 0

(x+5)/(25*x^2-10*x)+(x+4)/(20*x^2+8*x)-9/(25*x^2-4) = 0

25*x^2-10*x = 0

25*x^2-10*x = 0

5*x*(5*x-2) = 0

5*x-2 = 0 // + 2

5*x = 2 // : 5

x = 2/5

5*x*(x-2/5) = 0

20*x^2+8*x = 0

20*x^2+8*x = 0

4*x*(5*x+2) = 0

5*x+2 = 0 // - 2

5*x = -2 // : 5

x = -2/5

4*x*(x+2/5) = 0

(x+5)/(5*x*(x-2/5))+(x+4)/(4*x*(x+2/5))-9/(25*x^2-4) = 0

(4*x*(x+5)*(x+2/5)*(25*x^2-4))/(4*5*x*x*(x-2/5)*(x+2/5)*(25*x^2-4))+(5*x*(x+4)*(x-2/5)*(25*x^2-4))/(4*5*x*x*(x-2/5)*(x+2/5)*(25*x^2-4))+(-9*4*5*x*x*(x-2/5)*(x+2/5))/(4*5*x*x*(x-2/5)*(x+2/5)*(25*x^2-4)) = 0

4*x*(x+5)*(x+2/5)*(25*x^2-4)+5*x*(x+4)*(x-2/5)*(25*x^2-4)-9*4*5*x*x*(x-2/5)*(x+2/5) = 0

225*x^5+990*x^4-180*x^4-36*x^3-792/5*x^2+144/5*x^2 = 0

225*x^5+810*x^4-36*x^3-648/5*x^2 = 0

225*x^5+810*x^4-36*x^3-648/5*x^2 = 0

9*x^2*(25*x^3+90*x^2-4*x-72/5) = 0

25*x^3+90*x^2-4*x-72/5 = 0

25*x^3+90*x^2-4*x-72/5 = 0 // * 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 12, -12, 18, -18, 24, -24, 36, -36, 72, -72 }

1

x = 1

125*x^3+450*x^2-20*x-72 = 483

1

-1

x = -1

125*x^3+450*x^2-20*x-72 = 273

-1

2

x = 2

125*x^3+450*x^2-20*x-72 = 2688

2

-2

x = -2

125*x^3+450*x^2-20*x-72 = 768

-2

3

x = 3

125*x^3+450*x^2-20*x-72 = 7293

3

-3

x = -3

125*x^3+450*x^2-20*x-72 = 663

-3

4

x = 4

125*x^3+450*x^2-20*x-72 = 15048

4

-4

x = -4

125*x^3+450*x^2-20*x-72 = -792

-4

6

x = 6

125*x^3+450*x^2-20*x-72 = 43008

6

-6

x = -6

125*x^3+450*x^2-20*x-72 = -10752

-6

8

x = 8

125*x^3+450*x^2-20*x-72 = 92568

8

-8

x = -8

125*x^3+450*x^2-20*x-72 = -35112

-8

9

x = 9

125*x^3+450*x^2-20*x-72 = 127323

9

-9

x = -9

125*x^3+450*x^2-20*x-72 = -54567

-9

12

x = 12

125*x^3+450*x^2-20*x-72 = 280488

12

-12

x = -12

125*x^3+450*x^2-20*x-72 = -151032

-12

18

x = 18

125*x^3+450*x^2-20*x-72 = 874368

18

-18

x = -18

125*x^3+450*x^2-20*x-72 = -582912

-18

24

x = 24

125*x^3+450*x^2-20*x-72 = 1986648

24

-24

x = -24

125*x^3+450*x^2-20*x-72 = -1468392

-24

36

x = 36

125*x^3+450*x^2-20*x-72 = 6414408

36

-36

x = -36

125*x^3+450*x^2-20*x-72 = -5248152

-36

72

x = 72

125*x^3+450*x^2-20*x-72 = 48987288

72

-72

x = -72

125*x^3+450*x^2-20*x-72 = -44321832

-72

{ 1/5, -1/5, 1/25, -1/25, 1/125, -1/125, -1/5, 1/5, -1/25, 1/25, -1/125, 1/125, 2/5, -2/5, 2/25, -2/25, 2/125, -2/125, -2/5, 2/5, -2/25, 2/25, -2/125, 2/125, 3/5, -3/5, 3/25, -3/25, 3/125, -3/125, -3/5, 3/5, -3/25, 3/25, -3/125, 3/125, 4/5, -4/5, 4/25, -4/25, 4/125, -4/125, -4/5, 4/5, -4/25, 4/25, -4/125, 4/125, 6/5, -6/5, 6/25, -6/25, 6/125, -6/125, -6/5, 6/5, -6/25, 6/25, -6/125, 6/125, 8/5, -8/5, 8/25, -8/25, 8/125, -8/125, -8/5, 8/5, -8/25, 8/25, -8/125, 8/125, 9/5, -9/5, 9/25, -9/25, 9/125, -9/125, -9/5, 9/5, -9/25, 9/25, -9/125, 9/125, 12/5, -12/5, 12/25, -12/25, 12/125, -12/125, -12/5, 12/5, -12/25, 12/25, -12/125, 12/125, 18/5, -18/5, 18/25, -18/25, 18/125, -18/125, -18/5, 18/5, -18/25, 18/25, -18/125, 18/125, 24/5, -24/5, 24/25, -24/25, 24/125, -24/125, -24/5, 24/5, -24/25, 24/25, -24/125, 24/125, 36/5, -36/5, 36/25, -36/25, 36/125, -36/125, -36/5, 36/5, -36/25, 36/25, -36/125, 36/125, 72/5, -72/5, 72/25, -72/25, 72/125, -72/125, -72/5, 72/5, -72/25, 72/25, -72/125, 72/125 }

1/5

x

1/5

125*x^3+450*x^2-20*x-72 = -57

1/5

-1/5

x

-1/5

125*x^3+450*x^2-20*x-72 = -51

-1/5

1/25

x

1/25

125*x^3+450*x^2-20*x-72 = -72.072

1/25

-1/25

x

-1/25

125*x^3+450*x^2-20*x-72 = -70.488

-1/25

1/125

x

1/125

125*x^3+450*x^2-20*x-72 = -72.131136

1/125

-1/125

x

-1/125

125*x^3+450*x^2-20*x-72 = -71.811264

-1/125

-1/5

x

-1/5

125*x^3+450*x^2-20*x-72 = -51

-1/5

1/5

x

1/5

125*x^3+450*x^2-20*x-72 = -57

1/5

-1/25

x

-1/25

125*x^3+450*x^2-20*x-72 = -70.488

-1/25

1/25

x

1/25

125*x^3+450*x^2-20*x-72 = -72.072

1/25

-1/125

x

-1/125

125*x^3+450*x^2-20*x-72 = -71.811264

-1/125

1/125

x

1/125

125*x^3+450*x^2-20*x-72 = -72.131136

1/125

2/5

x

2/5

125*x^3+450*x^2-20*x-72 = 0

2/5

x-2/5

125*x^2+500*x+180

125*x^3+450*x^2-20*x-72

x-2/5

50*x^2-125*x^3

500*x^2-20*x-72

200*x-500*x^2

180*x-72

72-180*x

0

125*x^2+500*x+180 = 0

DELTA = 500^2-(4*125*180)

DELTA = 160000

DELTA > 0

x = (160000^(1/2)-500)/(2*125) or x = (-160000^(1/2)-500)/(2*125)

x = -2/5 or x = -18/5

x in { -18/5, -2/5, 2/5} 

9*x^2*(x+18/5)*(x+2/5)*(x-2/5) = 0

(9*x^2*(x+18/5)*(x+2/5)*(x-2/5))/(4*5*x*x*(x-2/5)*(x+2/5)*(25*x^2-4)) = 0

(9*x^2*(x+18/5)*(x+2/5)*(x-2/5))/(4*5*x*x*(x-2/5)*(x+2/5)*(25*x^2-4)) = 0 // * 4*5*x*x*(x-2/5)*(x+2/5)*(25*x^2-4)

9*x^2*(x+18/5)*(x+2/5)*(x-2/5) = 0

( 9*x^2 )

9*x^2 = 0 // : 9

x^2 = 0

x = 0

( x+18/5 )

x+18/5 = 0 // - 18/5

x = -18/5

( x+2/5 )

x+2/5 = 0 // - 2/5

x = -2/5

( x-2/5 )

x-2/5 = 0 // + 2/5

x = 2/5

x in { 0} 

x in { -2/5} 

x in { 2/5} 

x = -18/5

See similar equations:

| x^2+6x+30=0 | | x^2+2*x=0 | | y^2-64y+3724=0 | | x+3+5=0 | | y=1/2 | | 0.2p=4 | | -256=(X+-32)(X+-32) | | -64X+X^2=-1280 | | 16X-0.25X^2=320 | | 1-2x=y | | 12x-164=6x-14 | | 62-4x=23x+10 | | 3x+11=-28-10z | | 21/9=27/B | | 1/x+6 | | 5.76-4.24y-1.9y=27.864 | | 4.22-6.4x+9.6=0.38 | | -3x-21= | | 88-4x=22+2x | | 53-3x=23+7x | | 53-3x=23+7 | | ln(4x)+ln(2+x)=2 | | (x+11)-1=0 | | (x+11)-(x+11)-1=0 | | 10x-16=5x+17 | | (d-4/4)^2=100 | | 0=7x^2+18x-9 | | 1/3(2x-1)=-1/2x+7/6 | | 109-6x=12x+21 | | 11-8x=115-36x | | 13-8x=173-33x | | 76+3x=8x+21 |

(x+5)/(25x^2-10x)+(x+4)/(20x^2+8x)=9/(25x^2-4)

Simple and best practice solution for (x+5)/(25x^2-10x)+(x+4)/(20x^2+8x)=9/(25x^2-4) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

Solution for (x+5)/(25x^2-10x)+(x+4)/(20x^2+8x)=9/(25x^2-4) equation:

See similar equations:

Equations solver categories