How do you solve #\frac{5}{x^{2}+6x-7}-\frac{3}{x-1}=\frac{9}{3x+21}#?

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Answer 1 · 2018-01-23T04:49:19

#5/(x^2+6x-7) - 3/(x-1) = 9/(3x+21)#

#5/((x+7)(x-1)) - 3/(x-1) = 9/(3(x+7))#

Let's get an common denominator

#3/3 xx 5/((x+7)(x-1)) - 3/(x-1) xx (3)/(3) xx (x+7)/(x+7) = 9/(3(x+7)) xx (x-1)/(x-1)#

#15/(3(x+7)(x-1)) - (9(x-1)(x+7))/(3(x-1)(x+7)) = (9(x-1))/(3(x-1)(x+7)#

#(15 - 9x^2-55x+64)/(3(x+7)(x-1)) = (9x-9)/(3(x+7)(x-1))#

#-9x^2+55x-79 = 9x-9#

#-9x^2+46x - 70= 0#