How do you solve this rational expression?

Question

8/4-5p - 2/5p-4 + p-4/5p²+16p-16.

Perform operations and simplify.

Answer 1

Rachel

Factorise the quadratic first = (5p+4) (p-4)

Then the 3rd term simplifies to 1/5p+4

So you have 8/4-5p + 2/5p-4 + 1/5p+4

1st and 2nd terms are similar here, denominators have terms reversed so

8/4-5p = -8/ 5p-4

So combining first two gives -6/5p-4

So -6/5p-4 + 1 /5p+4

Now put these over a common denominator (5p-4) (5p+4)

(a+b) (a-b) = a²-b². So with a=5p, b = 4, this works out to 25p²-16

On the top : -6 (5p+4) + 1 (5p-4) = -25p - 29

So final result (-25p-29) / (25p²-16)

Mike