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# Algebra

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Find all the solutions to (x + 4)/(x + 5) = (x - 5)/(2x - 5)

Jun 11, 2021

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(x + 4)/(x + 5) = (x - 5)/(2x - 5)

First recognise that you cannot divide by 0

so   x cannot be -5 or   -2.5

then

$$\frac{(x + 4)}{(x + 5)} =\frac{ (x - 5)}{(2x - 5)}\\ \frac{(x + 4)}{(x + 5)} *\frac{(2x-5)}{(2x-5)}=\frac{ (x - 5)}{(2x - 5)}*\frac{(x+5)}{(x+5)}\\ \text{Now the denominators are the same so the numerators must be equal}\\ (x+4)(2x-5)=(x-5)(x+5)$$

expand both sides independently, collect like terms etc

Jun 11, 2021