How do you solve #\frac { 7x } { x - 1} - \frac { 8x } { x - 9} = \frac { 4} { x ^ { 2} - 10x + 9}#?

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Answer 1 · 2018-06-11T13:56:08

#x=-15 and x=-9#

Factoring: gives you
#(x^2-10x+9)=(x-9)xx(x-1)#

Therefore the original question:

#(7x)/(x-1) - (8x)/(x-9) = 4/(x^2-10x+9)#

can easily be solved by multiplying both sides with

#(x-1)xx(x-9)#, and then solving for #x#: :

#7x(x-9) - 8x(x-1) = 4#

#7x^2-36x-8x^2+8x-4=0#

#-(x^2+24x+4)=0#

#x^2+24x+4=0#

again, factoring gives you the two solutions for #x#:

#x=(-24+-sqrt(24^2-4xx4xx1))/(2xx1) = (-24+-6)/2 = #

#-> x=-15 and x=-9#