How do you solve #(x - 3) / (x - 4) = (x - 5 )/( x + 4)#?

1 Answer
Jun 5, 2018

Answer:

#x=16/5#

Explanation:

Given:

#(x-3)/(x-4) = (x-5)/(x+4)#

Multiply both sides by #(x-4)(x+4)# to get:

#(x-3)(x+4) = (x-5)(x-4)#

Multiplying out, this becomes:

#x^2+x-12 = x^2-9x+20#

Adding #-x^2+9x+12# to both sides, this becomes:

#10x = 32#

Dividing both sides by #10#, we find:

#x = 32/10 = 16/5#

Note that this value of #x# results in non-zero values of #(x-4)# and #(x+4)# so is a valid solution of the given rational equation.