Mister Exam
Expression simplification/
Least common denominator/
sqrt(x-a)/sqrt(x+a)-sqrt(x-a)-sqrt(x+a)/sqrt(x+a)-sqrt(x-a)
Least common denominator sqrt(x-a)/sqrt(x+a)-sqrt(x-a)-sqrt(x+a)/sqrt(x+a)-sqrt(x-a)
The solution
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_______ _______ \/ x - a _______ \/ x + a _______ --------- - \/ x - a - --------- - \/ x - a _______ _______ \/ x + a \/ x + a
$$- \sqrt{- a + x} + \left(\left(- \sqrt{- a + x} + \frac{\sqrt{- a + x}}{\sqrt{a + x}}\right) - \frac{\sqrt{a + x}}{\sqrt{a + x}}\right)$$
sqrt(x - a)/sqrt(x + a) - sqrt(x - a) - sqrt(x + a)/sqrt(x + a) - sqrt(x - a)
General simplification
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_______
_______ \/ x - a
-1 - 2*\/ x - a + ---------
_______
\/ a + x
$$- 2 \sqrt{- a + x} + \frac{\sqrt{- a + x}}{\sqrt{a + x}} - 1$$
-1 - 2*sqrt(x - a) + sqrt(x - a)/sqrt(a + x)
Common denominator
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_______
_______ \/ x - a
-1 - 2*\/ x - a + ---------
_______
\/ a + x
$$- 2 \sqrt{- a + x} + \frac{\sqrt{- a + x}}{\sqrt{a + x}} - 1$$
-1 - 2*sqrt(x - a) + sqrt(x - a)/sqrt(a + x)
Powers
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_______
_______ \/ x - a
-1 - 2*\/ x - a + ---------
_______
\/ a + x
$$- 2 \sqrt{- a + x} + \frac{\sqrt{- a + x}}{\sqrt{a + x}} - 1$$
-1 - 2*sqrt(x - a) + sqrt(x - a)/sqrt(a + x)
Rational denominator
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_______ _______ _______ _______
-a - x + \/ a + x *\/ x - a - 2*a*\/ x - a - 2*x*\/ x - a
------------------------------------------------------------
a + x
$$\frac{- 2 a \sqrt{- a + x} - a - 2 x \sqrt{- a + x} - x + \sqrt{- a + x} \sqrt{a + x}}{a + x}$$
(-a - x + sqrt(a + x)*sqrt(x - a) - 2*a*sqrt(x - a) - 2*x*sqrt(x - a))/(a + x)
Numerical answer
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-1 - 2*(x - a)^0.5 + (a + x)^(-0.5)*(x - a)^0.5
-1 - 2*(x - a)^0.5 + (a + x)^(-0.5)*(x - a)^0.5
Combinatorics
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/ _______ _______ _______ _______\
-\\/ a + x - \/ x - a + 2*\/ a + x *\/ x - a /
-------------------------------------------------
_______
\/ a + x
$$- \frac{2 \sqrt{- a + x} \sqrt{a + x} - \sqrt{- a + x} + \sqrt{a + x}}{\sqrt{a + x}}$$
-(sqrt(a + x) - sqrt(x - a) + 2*sqrt(a + x)*sqrt(x - a))/sqrt(a + x)
Trigonometric part
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_______
_______ \/ x - a
-1 - 2*\/ x - a + ---------
_______
\/ a + x
$$- 2 \sqrt{- a + x} + \frac{\sqrt{- a + x}}{\sqrt{a + x}} - 1$$
-1 - 2*sqrt(x - a) + sqrt(x - a)/sqrt(a + x)
Assemble expression
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_______
_______ \/ x - a
-1 - 2*\/ x - a + ---------
_______
\/ a + x
$$- 2 \sqrt{- a + x} + \frac{\sqrt{- a + x}}{\sqrt{a + x}} - 1$$
-1 - 2*sqrt(x - a) + sqrt(x - a)/sqrt(a + x)
Combining rational expressions
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_______ _______ / _______\ _______ _______
- \/ a + x + \/ x - a *\1 - \/ a + x / - \/ a + x *\/ x - a
-------------------------------------------------------------
_______
\/ a + x
$$\frac{\left(1 - \sqrt{a + x}\right) \sqrt{- a + x} - \sqrt{- a + x} \sqrt{a + x} - \sqrt{a + x}}{\sqrt{a + x}}$$
(-sqrt(a + x) + sqrt(x - a)*(1 - sqrt(a + x)) - sqrt(a + x)*sqrt(x - a))/sqrt(a + x)