We have, 7x 14 17(2x 1 x2)=4 7x 14 (4x 1+x14)=4 7x 14 (3x 114)=4 49x 7 6x+228=4 43x 528=4 43x 5=112 43x=117 x=11743 Hence ...

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Integration by Partial Fractions

7x-14-172x-1-...

Question

$\frac{7 x - 1}{4} - \frac{1}{7} (2 x - \frac{1 - x}{2}) = 4$

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Solution

We have,
$\frac{7 x - 1}{4} - \frac{1}{7} (2 x - \frac{1 - x}{2}) = 4$
$\frac{7 x - 1}{4} - (\frac{4 x - 1 + x}{14}) = 4$
$\frac{7 x - 1}{4} - (\frac{3 x - 1}{14}) = 4$
$\frac{49 x - 7 - 6 x + 2}{28} = 4$
$\frac{43 x - 5}{28} = 4$
$43 x - 5 = 112$
$43 x = 117$
$x = \frac{117}{43}$

Hence, this is the answer.

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