$$\frac{1}{a-1}+\frac{3}{4}=\frac{4}{a-1}$$
$a=5$
$$4+4\left(a-1\right)\times \frac{3}{4}=4\times 4$$
$$4+3\left(a-1\right)=4\times 4$$
$$4+3a-3=4\times 4$$
$$1+3a=4\times 4$$
$$1+3a=16$$
$$3a=16-1$$
$$3a=15$$
$$a=\frac{15}{3}$$
$$a=5$$
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