$$\frac{(2+x)(7-x)}{(5-x)(4+x)}=1$$
$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$
$$\left(2+x\right)\left(7-x\right)=\left(x-5\right)\left(-x-4\right)$$
$$14+5x-x^{2}=\left(x-5\right)\left(-x-4\right)$$
$$14+5x-x^{2}=-x^{2}+x+20$$
$$14+5x-x^{2}+x^{2}=x+20$$
$$14+5x=x+20$$
$$14+5x-x=20$$
$$14+4x=20$$
$$4x=20-14$$
$$4x=6$$
$$x=\frac{6}{4}$$
$$x=\frac{3}{2}$$
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