Step-by-step Solution

Simplify the expression $\frac{-x^2+2x+1}{4x-3}$

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$-\frac{1}{4}x+\frac{5}{16}+\frac{\frac{31}{16}}{4x-3}$

Step-by-step explanation

Problem to solve:

$\frac{-x^2+2x+1}{4x-3}$
1

Divide $-x^2+2x+1$ by $4x-3$

$\begin{array}{l}\phantom{\phantom{;}4x\phantom{;}-3;}{-\frac{1}{4}x\phantom{;}+\frac{5}{16}\phantom{;}\phantom{;}}\\\phantom{;}4x\phantom{;}-3\overline{\smash{)}-x^{2}+2x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x\phantom{;}-3;}\underline{\phantom{;}x^{2}-\frac{3}{4}x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{2}-\frac{3}{4}x\phantom{;};}\phantom{;}\frac{5}{4}x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}-3-;x^n;}\underline{-\frac{5}{4}x\phantom{;}+\frac{15}{16}\phantom{;}\phantom{;}}\\\phantom{;-\frac{5}{4}x\phantom{;}+\frac{15}{16}\phantom{;}\phantom{;}-;x^n;}\phantom{;}\frac{31}{16}\phantom{;}\phantom{;}\\\end{array}$
2

Resulting polynomial

$-\frac{1}{4}x+\frac{5}{16}+\frac{\frac{31}{16}}{4x-3}$

$-\frac{1}{4}x+\frac{5}{16}+\frac{\frac{31}{16}}{4x-3}$
$\frac{-x^2+2x+1}{4x-3}$