simplify: x^2-3x-28/x^2-9x+14. assume that the denominator is not equal to 0.?

Question

a. x-7/x-2 b. x-4/x+2 c. x-4/x-7 d. x+4/x-2

Answer 1

[x^2 - 3x - 28] / [x^2 - 9x + 14]

First, factor both of these quadratics.

[(x - 7)(x + 4)] / [(x - 7) (x - 2)]

Now, look at the factors common to both numerator and denominator. Cancel the common factor of (x - 7). This leaves us with

(x + 4) / (x - 2)

Answer 2

x^2 - 3x - 28 factors to (x -7)(x + 4)
x^2 -9x + 14 factors to (x -7)(x - 2)

so:

(x-7)(x+4)/(x-7)(x-2) = (x+4)/(x-2)

x <> 2 and x <> 7

Hope this helps!

Answer 3

Factor both the numerator and the denominator.

The multiple choice answers give you clues as to what the factors could be.

There will be a common term. Cancel it out.

Answer 4

The correct answer is d

i. x2-3x-38
___________
x2-9x+14

ii. (x-7)(x+4)
___________

(x-7)(x-2)

iii. (x+4)
_______
(x-2) (option d)