Question

If (x+5):(x+7)=(x-1):(x+2) find the value of x

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Answer 1

Answer:

The original equation can be expressed as

((x-5) (x+4))((x-7)(x+6))=504

Which when simplified gives,

(x^2-x-20)(x^2-x-42)=504

Put t= x^2-x

t^2-62x+336=0

Solving the quadratic, we get t=56 or 6

Hence x^2-x-56=0

So x=7,-8

And x^2-x-6=0

So, x=-2, 3

Hence x=7,-8,-2,3

Answer 2

Answer:

$\frac{(x + 5)}{(x + 7)} = \frac{(x - 1)}{(x + 2)} \\ \\ (x + 5)(x + 2) = (x - 1)(x + 7) \\ \\ {x}^{2} + 2x + 5x + 10 = {x}^{2} + 7x - x - 7 \\ \\ {x}^{2} + 7x + 10 = {x}^{2} + 6x - 7 \\ \\ {x}^{2} - {x}^{2} + 7x - 6x = - 7 - 10 \\ \\ x = - 17$

hope it helps you :)