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Surds and Indices Practice Test 2

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Question : 2 of 17

Marks: +1, -0

\frac{1}{1+a^{n-m}}+\frac{1}{1+a^{m-n}}=\text{?}

$a^{m+n}$
1
$\frac{1}{2}$
0

Solution:

Concept:

The two exponent terms are reciprocals, so their fractional denominators simplify to the same sum.

Explanation:

Let

a^{n-m}=x

.

Then

a^{m-n}=\frac{1}{x}

.

The expression becomes

\frac{1}{1+x}+\frac{1}{1+\frac{1}{x}}

.

Now,

\frac{1}{1+\frac{1}{x}}=\frac{x}{x+1}

.

So,

\frac{1}{1+x}+\frac{x}{x+1}=\frac{1+x}{1+x}=1

.

Answer:

The required value is

1

.

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