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Simplify the expression $\frac{x-y}{\left(\frac{1}{2}+\frac{-x}{2y}\right)\left(\sqrt{x-y}-\sqrt{x+y}\right)}$

Step-by-step Solution

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Final Answer

$\frac{-2y}{\sqrt{x-y}-\sqrt{x+y}}$
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Step-by-step Solution

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Combine $\frac{1}{2}+\frac{-x}{2y}$ in a single fraction

$\frac{x-y}{\frac{-x+y}{2y}\left(\sqrt{x-y}-\sqrt{x+y}\right)}$

Learn how to solve polynomial long division problems step by step online.

$\frac{x-y}{\frac{-x+y}{2y}\left(\sqrt{x-y}-\sqrt{x+y}\right)}$

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Learn how to solve polynomial long division problems step by step online. Simplify the expression (x-y)/((1/2+(-x)/(2y))((x-y)^1/2-(x+y)^1/2)). Combine \frac{1}{2}+\frac{-x}{2y} in a single fraction. Multiplying the fraction by \sqrt{x-y}-\sqrt{x+y}. Divide fractions \frac{x-y}{\frac{\left(-x+y\right)\left(\sqrt{x-y}-\sqrt{x+y}\right)}{2y}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Simplify \frac{2\left(x-y\right)y}{\left(-x+y\right)\left(\sqrt{x-y}-\sqrt{x+y}\right)} multiplying the denominator by -1.

Final Answer

$\frac{-2y}{\sqrt{x-y}-\sqrt{x+y}}$

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SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeSolve by quadratic formula (general formula)Find break even pointsFind the discriminant

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Plotting: $\frac{-2y}{\sqrt{x-y}-\sqrt{x+y}}$

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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

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Main Topic: Polynomial long division

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.

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