Question

12) Add the fractions, and simplify if possible. (y+7)/(y^2-y-12) - 2/(y^2-9)

Answer 1

Simplified form of $\frac{(y+7)}{(y^2-y-12)}-\frac{2}{(y^2-9)}$ is $\frac{y^2+2y-13}{(y-4)(y-3)(y+3)}$

Step-by-step explanation:

Add and simplify the fractions:

$\frac{(y+7)}{(y^2-y-12)}-\frac{2}{(y^2-9)}$

For Solving, First factor out the denominators:

Factoring: $y^2-y-12$

$y^2-y-12\\=y^2-4y+3y-12\\=y(y-4)+3(y-4)\\=(y-4)(y-3)$

Factoring: $y^2-9$

$y^2-9\\=(y)^2-(3)^2\\=(y-3)(y+3)$

Putting factors in the denominators:

$\frac{(y+7)}{(y-4)(y-3)}-\frac{2}{(y+3)(y-3)}$

Now taking LCM of (y-4)(y-3) and (y+3)(y-3): (y-4)(y-3)(y+3)

$\frac{(y+7)*(y-3)-2((y-4))}{(y-4)(y-3)(y+3)}\\=\frac{y^2-3y+7y-21-2y+8}{(y-4)(y-3)(y+3)}\\=\frac{y^2+2y-13}{(y-4)(y-3)(y+3)}$

So, Simplified form of $\frac{(y+7)}{(y^2-y-12)}-\frac{2}{(y^2-9)}$ is $\frac{y^2+2y-13}{(y-4)(y-3)(y+3)}$

Keywords: Adding the fractions

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