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Question

Divide the following and write your answer in lowest terms: x24x5x225÷x23x10x2+7x+10

A
x+1x5
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B
x1x5
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C
x+1x+5
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D
None of these
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Solution

The correct option is D x+1x5
The given expression x24x5x225÷x23x10x2+7x+10can be simplified as shown below:

=x24x5x225÷x23x10x2+7x+10

=x24x5x225×x2+7x+10x23x10

=x25x+x5x252×x2+5x+2x+10x25x+2x10

=x(x5)+1(x5)(x5)(x+5)×x(x+5)+2(x+5)x(x5)+2(x5)(a2b2=(ab)(a+b))

=(x+1)(x5)(x5)(x+5)×(x+2)(x+5)(x+2)(x5)

=(x+1)(x5)(x+2)(x+5)(x5)(x+5)(x+2)(x5)

=x+1x5

Hence, x24x5x225÷x23x10x2+7x+10=x+1x5.

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