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d+1/d=d+9/4d-3
We move all terms to the left:
d+1/d-(d+9/4d-3)=0
Domain of the equation: d!=0
d∈R
Domain of the equation: 4d-3)!=0We get rid of parentheses
d∈R
d+1/d-d-9/4d+3=0
We calculate fractions
d-d+4d/4d^2+(-9d)/4d^2+3=0
We add all the numbers together, and all the variables
4d/4d^2+(-9d)/4d^2+3=0
We multiply all the terms by the denominator
4d+(-9d)+3*4d^2=0
Wy multiply elements
12d^2+4d+(-9d)=0
We get rid of parentheses
12d^2+4d-9d=0
We add all the numbers together, and all the variables
12d^2-5d=0
a = 12; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·12·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{25}=5$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*12}=\frac{0}{24} =0 $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*12}=\frac{10}{24} =5/12 $
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