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Maths-

General

Easy

Question

$fraction numerator 1 over denominator 2 x plus 1 end fraction plus 5$
Which of the following is equivalent to the expression above for x > 0 ?

$\frac{2 x + 5}{2 x + 1}$
$\frac{2 x + 6}{2 x + 1}$
$\frac{10 x + 5}{2 x + 1}$
$\frac{10 x + 6}{2 x + 1}$

The correct answer is: $fraction numerator 10 x plus 6 over denominator 2 x plus 1 end fraction$

○        The concept used in this question is of algebraic expressions or expressions.
○        The algebraic expression is any mathematical statement. It is consists of numbers, variables and an arithmetic operation between them.
○        Expressions do not have fixed value.
○        The value can be get by just putting number is place of variables.

Step by step explanation:

Given:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator 1 over denominator 2 x plus 1 end fraction plus 5 end cell row cell not stretchy rightwards double arrow fraction numerator 1 over denominator 2 x plus 1 end fraction plus 5 over 1 end cell end table$
○        Step 1:
First make denominator equal
Multiply $5 over 1 text by end text fraction numerator left parenthesis 2 x plus 1 right parenthesis over denominator left parenthesis 2 x plus 1 right parenthesis end fraction$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator 1 over denominator 2 x plus 1 end fraction plus fraction numerator 5 cross times left parenthesis 2 x plus 1 right parenthesis over denominator 2 x plus 1 end fraction end cell row cell not stretchy rightwards double arrow fraction numerator 1 over denominator 2 x plus 1 end fraction plus fraction numerator left parenthesis 10 x plus 5 right parenthesis over denominator 2 x plus 1 end fraction end cell row cell not stretchy rightwards double arrow fraction numerator 1 plus 10 x plus 5 over denominator 2 x plus 1 end fraction end cell row cell not stretchy rightwards double arrow fraction numerator 10 x plus 6 over denominator 2 x plus 1 end fraction end cell end table$
Hence, the expression equivalent to $fraction numerator 1 over denominator 2 x plus 1 end fraction plus 5 text is end text fraction numerator 10 x plus 6 over denominator 2 x plus 1 end fraction$

Final Answer:

Correct option is,
Option D. $fraction numerator 10 x plus 6 over denominator 2 x plus 1 end fraction$

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