If a b = 1 then \;1+a/1+b is

Correct Answer is : 1−a1−b\;1-a/1-b1−b1−a

Correct Answer is : 1−a1−b\;1-a/1-b1−b1−a

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Ratio and Proportion

Question : 6 of 112

Marks: +1, -0

a b = 1

\;\frac{1+a}{1+b}

Solution:

Concept:

Simplify the given expression using the condition

ab=1

and compare with the options.

Explanation:

Given

ab=1

. Hence

b=\frac{1}{a}

Substitute

b

into

\frac{1+a}{1+b}

\frac{1+a}{1+\frac{1}{a}} = \frac{1+a}{\frac{a+1}{a}} = (1+a) \cdot \frac{a}{a+1} = a

Now test each option by using

b=\frac{1}{a}

Option C:

\frac{a-1}{1-b} = \frac{a-1}{1-\frac{1}{a}} = \frac{a-1}{\frac{a-1}{a}} = (a-1)\cdot\frac{a}{a-1} = a

This matches the simplified value

a

The other options simplify to

-a

\frac{1}{a}

, which are not equal to

a

Answer:

The correct option is C.

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