152k views
5 votes
Can you please tell me how to solve this????

Can you please tell me how to solve this????-example-1

1 Answer

0 votes

Answer:

-2

Explanation:

You have to simplify numerator and denominator through factoring. The you should get an expression involving only a + b which is given as -2

Take numerator

a^2-b^2-12b-36

Factor

-b^2-12b-36


= - (b^2 + 12b + 36)\\\\= -(b+6)^2

So numerator becomes

a^2-\left(b+6\right)^2

Apply difference of squares formula:
\displaystyle x^2-y^2=\left(x+y\right)\left(x-y\right)


\mathrm{with\;} x^2 == > a^2, and y^2 == > (b + 6)^2


\implies a^2-\left(b+6\right)^2 \\== \left(a+\left(b+6\right)\right)\left(a-b-6\right)

Denominator

a^2-6a-b^2-6b

can be factored as follows


a^2-b^2 = (a + b) (a -b)

-6a-6b = -6\left(a+b\right)

So denominator becomes

\left(a+b\right)\left(a-b\right)+-6\left(a+b\right)

Factor out common term (a+b) to get

\left(a+b\right)\left(a-b-6\right)

So the original expression with Numerator and denominator


\displaystyle =(\left(a+b+6\right)\left(a-b-6\right))/(\left(a+b\right)\left(a-b-6\right))
Cancel the common factor (a-b-6) to get

\displaystyle (a+b+6)/(a+b)

Since a + b = -2, plug in this value of (a+b) in both numerator and denominator to get

\displaystyle (-2 + 6)/(-2)

\displaystyle = - 2

Answer: -2





User Jules Copeland
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories