Rational expressions are expressions that can be represented as fractions
The solution to the sum of the rational expressions is [tex]\frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]
How to determine the error
The student operation is given as:
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac { 5 x } { x + 7 } + \frac { 7 ( 7 ) } { x + 7 } = \frac{5x + 49}{x + 7}[/tex]
The student's error is that, he multiplied the numerator of 7/x by 7, and he added 7 to the denominator
The correction is as follows:
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x }[/tex]
Take the LCM
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac{5x^2 + 7(x + 7)}{(x + 7)x}[/tex]
Open the brackets
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]
Hence, the solution to the sum of the rational expressions is [tex]\frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]
Read more about rational expressions at:
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