Step-by-step Solution

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

Go!
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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final Answer

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

Step-by-step explanation

Problem to solve:

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

$\frac{x-1}{x+3}$
$\frac{x^2+x-2}{x^2+5x+6}$

Time to solve it:

~ 0.04 s (SnapXam)