Reducing equations to simpliest form

Question

Perform the indicated operations and reduce the answer to lowest terms. These questions are on an optional practice test and I am completely lost.

A. (X³ + X / X² +X) x (X² - 1/ X² +1)

B. X / X+1 + 1 / X-1 + 1

C. 3 - 1/x / 9 - 1/x²

Answer 1

try to factor the factors and cancel factors that appear in both numerator and denominator

(x^3 +x)/(x^2+x) = (x)(x^2+1)/(x)(x+1) = (x^2+1)/(x+1) cancel the x's. x/x = 1

(x^2+1)/(x+1) x (x2-1)/(x^2+1) = (x^2+1)/(x^2+1) x (x^2-1)/(x+1) = 1 x (x^2-1)/(x+1) = (x^2-1)/(x+1) cancel the (x^2+1) factors then factor (x^2-1)(x+1) into (x+1)(x-1)/(x+1) = x-1

x-1 is the answer to part A

part B is a little ambiguous

the way it's written is really x/x - 1 + 1/x +1 + 1 = 2 + 1/x or (2x+1)/x,

but odds are it was possibly intended to be

x/(x-1) + 1/(x+1) + 1 but the parentheses got left out or were implicit

= x(x+1)/(x^2-1) + (x-1)/(x^2-1) + (x^2-1)/(x^2-1) (put each term over a common denominator, then add the numerators)

=(x^2+x +x-1 +x^2-1)/(x^2-1)

= (2x^2+2x-2)/(x^2-1) = 2(x^2+x-1)(x^2-1) or 2(x^2+x-1)/(x+1)(x-1)

Part C has a similar ambiguity, but given the spaces used

3 - 1/x/9 - 1/x^2 is probably meant to read as

(3-1)/x divided by (9-1)/x^2

=2/x divided by 8/x^2

= (2/x)(x^2/8 )= (2/8)(x^2/x) = (1/4)(x) = x/4

x/4 is the likely answer to Part C

but if you interpreted the problem as 3 -1/x/9 -1/x^2 that is = 3- 9/x -1/x^2 = 3x^2/x^2 -9x/x^2 - 1/x^2 =

(3x^2 -9x -1)/x^2 It's unlikely that's the answer. More likely spaces were implicit parentheses in the problem so x/4 is the expected answer