question_answer

Solve for \[x:\frac{(2+x)(7-x)}{(5-x)(4+x)}=1\]

Answer:

We have,

\[\frac{(2+x)(7-x)}{(5-x)(4+x)}=1\]

By cross-multiplication, we get

\[(2+x)(7x)=(5x)(4+x)\]

or,

\[2(7x)+x(7x)=5\text{ }(4+x)x(4+x)\]

or,

\[142x+7x{{x}^{2}}=20+5x4x{{x}^{2}}\]

or,

\[14+5x=20+x\]

or,

\[5xx=\text{ }2014\]

or,

\[4x=6\]

or, x =

\[\frac{6}{4}=\frac{3}{2}\]

Thus, the solution of the given equation is x =

\[\frac{3}{2}\]