How do you solve (x+3)/(x^(2)+3x-4)=(x+2)/(x^(2)-16)?

1 Answer
May 31, 2015

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

By property: color(blue)(a^2 - b^2 = (a+b)(a-b)

so, x^(2)-16 = color(blue)((x+4)(x-4)

By splitting the middle term,
x^2+3x-4 can be factorised as color(green)((x+4)(x-1)

now rewriting the expression
(x+3)/color(green)((cancelx+4)(x-1))=(x+2)/color(blue)(cancel(x+4)(x-4)

we get,
(x+3)/(x-1) = (x+2)/(x-4)

cross multiplying:
(x+3).(x-4) = (x+2).(x-1)
cancel x^2 -x -12 = cancelx^2 +x - 2
- 10 = 2x , color(red)(x =-5