Question

Write each fraction in terms of the LCD.

X-2
x2
X + 3x - 28
X
x + 9x + 14

Answer 1

a)
`(x^2-4)/((x + 7)(x - 4)(x+2))`

b)
`(x^2-4x)/((x + 7)(x + 2)(x-4))`

Explanation:

x² + 3x - 28

= x² + 7x - 4x -28

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

=

= x² + 7x + 2x + 14

= x(x + 7) + 2(x + 7)

= (x + 7)(x + 2)

LCM of x² + 3x - 28 and x² + 9x + 14 is

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

We can write:

`(x-2)/(x^2 + 3x - 28)\\ \\= (x-2)/((x + 7)(x - 4))\\\\= (x-2)/((x + 7)(x - 4)) *(x+2)/(x+2) \\\\=((x-2)(x+2))/((x + 7)(x - 4)(x+2)) \\\\=(x^2-2^2)/((x + 7)(x - 4)(x+2)) \\\\=(x^2-4)/((x + 7)(x - 4)(x+2))`

and

`(x)/(x^2 + 9x + 14 )\\ \\= (x)/((x + 7)(x + 2))\\\\= (x)/((x + 7)(x + 2)) *(x-4)/(x-4) \\\\= (x(x-4))/((x + 7)(x + 2)(x-4)) \\\\= (x^2-4x)/((x + 7)(x + 2)(x-4))`