Step-by-step Solution

Simplify the expression $\frac{x^2+x-2}{x^2+5x+6}$

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Final Answer

$\frac{x-1}{x+3}$
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Step-by-step Solution

Problem to solve:

$\frac{x^2+x-2}{x^2+5x+6}$

Choose the solving method

1

Factor the trinomial $x^2+x-2$ finding two numbers that multiply to form $-2$ and added form $1$

$\begin{matrix}\left(-1\right)\left(2\right)=-2\\ \left(-1\right)+\left(2\right)=1\end{matrix}$
2

Thus

$\frac{\left(x-1\right)\left(x+2\right)}{x^2+5x+6}$
3

Factor the trinomial $x^2+5x+6$ finding two numbers that multiply to form $6$ and added form $5$

$\begin{matrix}\left(2\right)\left(3\right)=6\\ \left(2\right)+\left(3\right)=5\end{matrix}$
4

Thus

$\frac{\left(x-1\right)\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}$
5

Simplifying

$\frac{x-1}{x+3}$

Final Answer

$\frac{x-1}{x+3}$
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0
a
b
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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

Tips on how to improve your answer:

$\frac{x^2+x-2}{x^2+5x+6}$

Time to solve it:

~ 0.06 s