Equivalent fractions- multiply both numerator and denominator by the same number. <span />
First one is -1. The second one is 1/2.
Answer:
D: 169
Step-by-step explanation:
because the number of dots along the bottom increases by two every time, the 7th one would have 13.
13 x 13 = 169
Looks like the integrand is
![\dfrac{-4x-34}{x^2+2x-8}](https://tex.z-dn.net/?f=%5Cdfrac%7B-4x-34%7D%7Bx%5E2%2B2x-8%7D)
The denominator is factorized as
![x^2+2x-8=(x+4)(x-2)](https://tex.z-dn.net/?f=x%5E2%2B2x-8%3D%28x%2B4%29%28x-2%29)
Then we want to find constants
such that
![-\dfrac{4x+34}{x^2+2x-8}=\dfrac A{x+4}+\dfrac B{x-2}](https://tex.z-dn.net/?f=-%5Cdfrac%7B4x%2B34%7D%7Bx%5E2%2B2x-8%7D%3D%5Cdfrac%20A%7Bx%2B4%7D%2B%5Cdfrac%20B%7Bx-2%7D)
![\implies-4x-34=A(x-2)+B(x+4)](https://tex.z-dn.net/?f=%5Cimplies-4x-34%3DA%28x-2%29%2BB%28x%2B4%29)
We can use the cover-up method to easily find
and
: