How do you simplify #\frac{x+1}{x+7}=\frac{x^{2}-51x}{x^{2}+5x-14}-\frac{x-7}{x-2}#?

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Answer 1 · 2016-09-28T13:27:26

#x = 1 and -51#

#(x+ 1)/(x + 7) = (x^2 - 51x )/((x + 7)(x- 2)) - (x - 7)/(x- 2)#

#((x + 1)(x - 2))/((x + 7)(x - 2)) = (x^2 - 51x)/((x + 7)(x - 2)) - ((x - 7)(x + 7))/((x- 2)(x + 7))#

You can now eliminate the denominators and solve.

#x^2 + x - 2x - 2 = x^2 - 51x - (x^2 - 49)#

#x^2 - x - 2 = x^2 - 51x -x^2 + 49#

#x^2 + 50x - 51 = 0#

#(x + 51)(x - 1) = 0#

#x = -51 and 1#

Hopefully this helps!