How do you simplify (x+2) /(4x^2 - 14x + 6)-(x+4)/(x^2 + x -12)?

1 Answer
Jun 16, 2016

= [-3x^2- 16x + 16]/[(x-3)(4x-2)(x+4)]

Explanation:

Factor first.

(x+2) / (4x^2-14x+6) -(x+4)/(x^2+x-12)

= (x+2)/((x-3)(4x-2)) - (x+4)/((x+4)(x-3))

Change to similar fractions by getting LCD = (x -3)(4x-2)(x-3)

= [(x+2)(x+4)]/((x-3)(4x-2)(x+4))- [(x +4)(4x - 2)]/((x-3)(4x-2)(x+4))

= ((x+2)(x+4)-(x+4)(4x-2))/((x-3)(4x-2)(x+4))

Use distributive property of multiplication.

=[(x^2 +4x + 2x + 8)-(4x^2 -2x +16x -8)]/[(x-3)(4x-2)(x+4)]

Combine like terms.

= [-3x^2- 8x + 16]/[(x-3)(4x-2)(x+4)]