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Solve the following:
$\frac{4 x-5}{8 x - 1}$=$ \frac{x+2}{2 x+1}$
Given:
$\frac{4 x-5}{8 x - 1}$=$ \frac{x+2}{2 x+1}$
To do: Find the value of the expression
Solution:
$\frac{4 x-5}{8 x - 1}$=$ \frac{x+2}{2 x+1}$
Cross multiplication
$4x-5(2x+1)= 8x-1(x+2)$
$4x(2x-1)-5(2x-1)=8x(x+2)-1(x+2)$
$8x^2-4x-10x+5=8x^2+16x-x-2$
$8x^2-14x+5=8x^2+15x-2$
$8x^2-8x^2-14x-15x=-5-2$
$-29x=-7$
$x=\frac{29}{7}$
Therefore the value of $x$ is $\frac{29}{7}$
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