How do you multiply (56+11x-16x^2)*10/(15x^2-11x-56)(56+11x16x2)1015x211x56 and state the excluded values?

1 Answer
May 7, 2018

(56+11x-16x^2)*10/(15x^2-11x-56)(56+11x16x2)1015x211x56

= - {160x^2 -110 x - 560}/{15x^2 -11 x - 56}=160x2110x56015x211x56

excluding x = -8/5 and x=7/3x=85andx=73

Explanation:

There's a 15x^215x2 in the denominator and a -16x^216x2 in the numerator, so the cancelling that we might hope for at first glance doesn't materialize.

The excluded values occur at the zeros of the denominator; let's try to factor. We seek a pair of factors of 1515 and a pair of factors of -5656 whose sum of products is -11.11. That's a bit of a search, we have

15=1\times 15= 3 \times 515=1×15=3×5

56=1\times 56= 2 \times 28 = 4 \times 14 = 7 \times 856=1×56=2×28=4×14=7×8 with a minus sign in there for -56.56.

Eventually we find -7\times 8=-56,7×8=56, 5 times 3 = 15,5×3=15, -7(5)+3(8)=-11 quad sqrt

15x^2 -11 x - 56 = (5 x + 8) (3 x - 7)

We could also have used the quadratic formula to find the zeros of the denominator, which are called poles.

x = -8/5 or x=7/3

The multiplication itself is rather vacuous due to the lack of cancelling.

(56+11x-16x^2)*10/(15x^2-11x-56)

= - {160x^2 -110 x - 560}/{15x^2 -11 x - 56}