How do you solve #\frac { 7x - 49} { 3x ^ { 2} + 6x - 72} + \frac { 1} { x + 6} = \frac { 5} { 3x - 12}#?

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Answer 1 · 2018-06-07T19:17:49

#x=91/5#

First factor the terms in the denominators:

#\frac { 7x - 49} { 3x ^ { 2} + 6x - 72} + \frac { 1} { x + 6} = \frac { 5} { 3x - 12}#

#(7x-49)/(3(x + 6)(x - 4))+1/(x+6)=5/(3(x-4))#

So we have common factors of #3(x + 6)(x - 4)# in the denominator, now we multiply the whole thing times the common denominator:

#3(x + 6)(x - 4)[(7x-49)/(3(x + 6)(x - 4))+1/(x+6)=5/(3(x-4))]#

now cancel out and multiply through using the distributive property:

#7x-49 + 3(x-4) = 5(x+6)#

#7x-49 + 3x-12 = 5x+30#

#10x -61 =5x+30#

#5x=91#

#x=91/5#