(9x+5)/(x^2-1)=4

Solution for (9x+5)/(x^2-1)=4 equation:

(9x+5)/(x^2-1)=4

We move all terms to the left:

(9x+5)/(x^2-1)-(4)=0


Domain of the equation: (x^2-1)!=0

We move all terms containing x to the left, all other terms to the right

x^2!=1

x^2!=1/

x^2!=√1/

x!=1

x∈R


We multiply all the terms by the denominator


(9x+5)-4*(x^2-1)=0

We multiply parentheses

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

We get rid of parentheses

-4x^2+9x+5+4=0

We add all the numbers together, and all the variables

-4x^2+9x+9=0

a = -4; b = 9; c = +9;
Δ = b2-4ac
Δ = 92-4·(-4)·9
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*-4}=\frac{6}{-8}
=-3/4
$