Question

integration
$( \sqrt{a - x} ) \div ( \sqrt{a + x} )$
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Answer 1

I guess this is maths but still i will answer

Rewrite the division as a fraction.

√a−x√a+x

Multiply √a−x√a+x

by √a+x√a+x

.

√a−x√a+x⋅√a+x√a+x

Combine and simplify the denominator.

Multiply √a−x√a+x

and √a+x√a+x

.

√a−x√a+x√a+x√a+x

Raise √a+x

to the power of 1

.

√a−x√a+x√a+x1√a+x

Raise √a+x

to the power of 1

.

√a−x√a+x√a+x1√a+x1

Use the power rule aman=am+n

to combine exponents.

√a−x√a+x√a+x1+1

Add 1

and 1

.

√a−x√a+x√a+x2

Rewrite √a+x2

as a+x

.

Rewrite √a+x

as (a+x)12

.

√a−x√a+x((a+x)12)2

Apply the power rule and multiply exponents, (am)n=amn

.

√a−x√a+x(a+x)12⋅2

Combine 12

and 2

.

√a−x√a+x(a+x)22

Cancel the common factor of 2

.

Tap for more steps...

√a−x√a+x(a+x)1

Simplify.

√a−x√a+xa+x

Combine using the product rule for radicals.

√(a−x)(a+x)a+x