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Simplify the expression $\frac{\frac{x^2+5x+6}{x^2-x-6}}{\frac{x^2+6x+9}{2x^2-5x-3}}$

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Solution

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Final answer to the problem

$\frac{2x^2-5x-3}{x^2-9}$
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Step-by-step Solution

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Simplify the fraction $\frac{\frac{x^2+5x+6}{x^2-x-6}}{\frac{x^2+6x+9}{2x^2-5x-3}}$

Learn how to solve factor by difference of squares problems step by step online.

$\frac{\left(x^2+5x+6\right)\left(2x^2-5x-3\right)}{\left(x^2-x-6\right)\left(x^2+6x+9\right)}$

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Learn how to solve factor by difference of squares problems step by step online. Simplify the expression ((x^2+5x+6)/(x^2-x+-6))/((x^2+6x+9)/(2x^2-5x+-3)). Simplify the fraction \frac{\frac{x^2+5x+6}{x^2-x-6}}{\frac{x^2+6x+9}{2x^2-5x-3}}. Factor the trinomial \left(x^2+5x+6\right) finding two numbers that multiply to form 6 and added form 5. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. Factor the trinomial \left(x^2-x-6\right) finding two numbers that multiply to form -6 and added form -1.

Final answer to the problem

$\frac{2x^2-5x-3}{x^2-9}$

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Function Plot

Plotting: $\frac{2x^2-5x-3}{x^2-9}$

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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
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

How to improve your answer:

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$2x\div x$

Main Topic: Factor by Difference of Squares

The difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2=(a+b)(a-b) in elementary algebra.

Used Formulas

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