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Simplify the expression $\frac{\left(\sqrt{a+5}-3\right)\left(\sqrt{a}+2\right)}{a-4}$

Step-by-step Solution

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Final Answer

$\sqrt{a+5}\sqrt{a}+2\sqrt{a+5}-3\sqrt{a}-6$
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Step-by-step Solution

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Multiply the single term $\sqrt{a}+2$ by each term of the polynomial $\left(\sqrt{a+5}-3\right)$

$\frac{\sqrt{a+5}\left(\sqrt{a}+2\right)-3\left(\sqrt{a}+2\right)}{a-4}$

Learn how to solve simplification of algebraic fractions problems step by step online.

$\frac{\sqrt{a+5}\left(\sqrt{a}+2\right)-3\left(\sqrt{a}+2\right)}{a-4}$

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Learn how to solve simplification of algebraic fractions problems step by step online. Simplify the expression (((a+5)^1/2-3)(a^1/2+2))/(a-4). Multiply the single term \sqrt{a}+2 by each term of the polynomial \left(\sqrt{a+5}-3\right). Multiply the single term -3 by each term of the polynomial \left(\sqrt{a}+2\right). Multiplying polynomials \sqrt{a+5} and \sqrt{a}+2.

Final Answer

$\sqrt{a+5}\sqrt{a}+2\sqrt{a+5}-3\sqrt{a}-6$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind ((a+5)^0.5-3)(a^0.5+2)/(a-4) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Function Plot

Plotting: $\frac{\sqrt{a+5}\sqrt{a}+2\sqrt{a+5}-3\sqrt{a}-6}{a-4}$

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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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