# Thread: Partial fractions

1. ## Partial fractions

Evaluate the values of a and b in the following:

a(2x + 3) + b(5 - x) = 4 - 6x

2. for $x = \frac{-3}{2}$

$a(0)+b\left(5-\frac{-3}{2}\right)=4-6\left(\frac{-3}{2}\right)$

$b\left(5-\frac{-3}{2}\right)=4-6\left(\frac{-3}{2}\right)$

$b=\frac{4-6(\frac{-3}{2})}{(5-\frac{-3}{2})}$

$b=\dots$

and for $x = 5$

$a(5\times5+3)=4-6\times 5$

$a=\frac{4-6\times 5}{(5\times5+3)}$

$a=\dots$

3. Originally Posted by Joker37
Evaluate the values of a and b in the following:

a(2x + 3) + b(5 - x) = 4 - 6x

$2ax+3a+5b-bx=4-6x$

$2ax-bx+3a+5b=4-6x$

$(2a-b)x+3a+5b=4-6x$

$3a+5b+(2a-b)x=4-6x$

By comparing ,

$3a+5b=4$--- 1

$2a-b=-6$ --- 2

Solve the system .