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

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Answer 1 · 2017-11-23T15:38:29

#x_1=1/15# and #x_2=-10/27#

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

#[(x-3)(9x+2)-(x+6)(9x-1)]/[(9x-1)(9x+2)]=5#

#[(9x^2-25x-6)-(9x^2+53x-6)]/(81x^2+9x-2)=5#

#(-78x)/(81x^2+9x-2)=5#

#5*(81x^2+9x-2)=-78x#

#405x^2+45x-10=-78x#

#405x^2+123x-10=0#

#Delta=123^2-4*405*(-10)=31329=177^2#

#x_1=(-123+177)/(2*405)=54/810=1/15#

#x_2=(-123-177)/(2*405)=(-300)/810=-10/27#