How do you solve #1/(x-4) + (x-4)/(x-4) = 7 / ( x^2+x-20)#?

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Answer 1 · 2017-06-19T17:26:16

Eliminate the denominators by multiplying both sides by #(x-4)(x+5)#.
Solve the resulting quadratic.

Given: #1/(x-4) + (x-4)/(x-4) = 7 / ( x^2+x-20)#

Eliminate the denominators by multiplying both sides by #(x-4)(x+5)#.

#x+5+(x-4)(x+5) = 7#

#x+5 + x^2+x-20 = 7#

#x^2+2x-22 = 0#

#x = (-2+-sqrt(2^2-4(1)(-22)))/(2(1))#

#x = (-2+-2sqrt(23))/2#

#x = -1+sqrt(23) and x = -1-sqrt(23)#

This agrees with WolframAlpha