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

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Answer 1 · 2018-06-05T05:50:52

$x=16/5$

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.

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