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alisha [4.7K]
3 years ago
7

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

Mathematics
1 answer:
Tanzania [10]3 years ago
5 0

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

Learn more about Adding the fractions at:

  • brainly.com/question/2456302
  • brainly.com/question/1648978
  • brainly.com/question/1757979

#learnwithBrainly

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