Test Index

Surds and Indices Practice Test 1

© examsnet.com

Question : 1 of 40

Marks: +1, -0

\frac{1}{1+x^{b-a}+x^{c-a}}+\frac{1}{1+x^{a-b}+x^{c-b}}+\frac{1}{1+x^{b-c}+x^{a-c}}=?

$x^{a+b+c}$
$x^{a-b-c}$
1
0

Solution:

Concept:

Use

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

to rewrite each term and combine them.

Explanation:

Let

A=x^a

,

B=x^b

, and

C=x^c

.

First term:

x^{b-a}=\frac{B}{A}

and

x^{c-a}=\frac{C}{A}

.

So

\frac{1}{1+x^{b-a}+x^{c-a}}=\frac{A}{A+B+C}

.

Second term:

x^{a-b}=\frac{A}{B}

and

x^{c-b}=\frac{C}{B}

.

So

\frac{1}{1+x^{a-b}+x^{c-b}}=\frac{B}{A+B+C}

.

Third term:

x^{b-c}=\frac{B}{C}

and

x^{a-c}=\frac{A}{C}

.

So

\frac{1}{1+x^{b-c}+x^{a-c}}=\frac{C}{A+B+C}

.

Adding all three terms gives

\frac{A+B+C}{A+B+C}=1

.

Answer:

The value of the expression is

1

, so the correct option is C.

© examsnet.com

Go to Question:

Next Question