y-2/y-9=7/y-9

Solution for y-2/y-9=7/y-9 equation:

y-2/y-9=7/y-9

We move all terms to the left:

y-2/y-9-(7/y-9)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: y-9)!=0

y∈R


We get rid of parentheses

y-2/y-7/y+9-9=0

We multiply all the terms by the denominator


y*y+9*y-9*y-2-7=0

We add all the numbers together, and all the variables

y*y-9=0

Wy multiply elements

y^2-9=0

a = 1; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·1·(-9)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*1}=\frac{-6}{2}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*1}=\frac{6}{2}
=3
$