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

Step-by-step Solution

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Final answer to the problem

$1+\frac{-1}{1+x^2}$
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Step-by-step Solution

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  • Write in simplest form
  • Solve by quadratic formula (general formula)
  • Find the derivative using the definition
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
  • Factor by completing the square
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1

Divide $x^2$ by $1+x^2$

$\begin{array}{l}\phantom{\phantom{;}x^{2}+1;}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+1\overline{\smash{)}\phantom{;}x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{2}+1;}\underline{-x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{-x^{2}-1\phantom{;}\phantom{;};}-1\phantom{;}\phantom{;}\\\end{array}$
2

Resulting polynomial

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

Final answer to the problem

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

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Function Plot

Plotting: $1+\frac{-1}{1+x^2}$

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

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

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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