Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

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

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Answer

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

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

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

Unlock this step-by-step solution!

Answer

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

Main topic:

Simplification of algebraic fractions

Time to solve it:

~ 0.56 seconds