How do you solve #\frac { 2} { x - 3} + \frac { 5} { x - 4} = \frac { 3} { x ^ { 2} - 7x + 12}#?

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Answer 1 · 2017-08-07T15:14:06

#color(magenta)(x=26/7#

#2/(x-3)+5/(x-4)=3/(x^2-7x+12)#

#:.2/(x-3)+5/(x-4)=3/((x-3)(x-4))#

#:.(2(x-4)+5(x-3)=3)/((x-3)(x-4))#

multiply both sides by #(x-3)(x-4)#

#:.2(x-4)+5(x-3)=3#

#:.2x-8+5x-15=3#

#:.7x-23=3#

#:.7x=3+23#

#:.7x=26#

#:.color(magenta)(x=26/7#

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check:

#:.2/((color(magenta)(26/7))-3)+5/((color(magenta)(26/7))-4)=3/((color(magenta)(26/7))^2-7(color(magenta)(26/7))+12)#

#:.2/(26/7-21/7)+5/(26/7-28/7)=3/((676/49)-26+12)#

#:.2/(5/7)+5/(-2/7)=3/((676/49)-14)#

#:.(2/1 xx 7/5)+(5/1 xx -7/2)=3/(676/49-686/49)#

#:.14/5-35/2=3/(-10/49)#

#:.14/5-35/2=3/1 xx -49/10#

#:.14/5-35/2=-147/10#

#:.(2(14)-5(35)=-147)/10#

multiply both sides by #10#

#:.2(14)-5(35)=-147#

#:.28-175=-147#

#:.color(magenta)(-147=-147#