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Simplify $\frac{x}{x^2+7x+10}+\frac{-1}{x^2+x-20}+\frac{2}{x^2-16}$

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{x^{3}-8x+x^2+12}{\left(x+2\right)\left(x+5\right)\left(x^2-16\right)}$
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Step-by-step Solution

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  • Write in simplest form
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Factor the trinomial $x^2+7x+10$ finding two numbers that multiply to form $10$ and added form $7$

$\begin{matrix}\left(2\right)\left(5\right)=10\\ \left(2\right)+\left(5\right)=7\end{matrix}$

Learn how to solve combining like terms problems step by step online.

$\begin{matrix}\left(2\right)\left(5\right)=10\\ \left(2\right)+\left(5\right)=7\end{matrix}$

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Learn how to solve combining like terms problems step by step online. Simplify x/(x^2+7x+10)+-1/(x^2+x+-20)2/(x^2-16). Factor the trinomial x^2+7x+10 finding two numbers that multiply to form 10 and added form 7. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. Factor the trinomial x^2+x-20 finding two numbers that multiply to form -20 and added form 1. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values.

Final answer to the problem

$\frac{x^{3}-8x+x^2+12}{\left(x+2\right)\left(x+5\right)\left(x^2-16\right)}$

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Function Plot

Plotting: $\frac{x^{3}-8x+x^2+12}{\left(x+2\right)\left(x+5\right)\left(x^2-16\right)}$

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x
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(◻)
+
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◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

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Similar Problems Solved

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Main Topic: Combining like terms

Algebraic expressions can be simplified by combining like terms.

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