What is 5 plus 3

Asked by maham237 @ 09/01/2021 in Mathematics viewed by 312 People

Classify the solutions of 3 over x plus 5, plus one fifth, equals 2 over x plus 5 as extraneous or non-extraneous.

Answered by maham237 @ 09/01/2021

The correct answer is:

non-extraneous

Explanation:

An extraneous solution is one that we arrive at that will not work in the equation. For rational equations such as we have, extraneous solutions are ones that will cause the denominator to be 0. For ours, that would mean x=-5.

The equation we have is:

$\frac{3}{x+5}+\frac{1}{5}=\frac{2}{x+5}$

We will multiply everything by (x+5) in order to get that off the bottom of the fractions:

$\frac{3}{x+5}\times (x+5)+\frac{1}{5}\times (x+5)=\frac{2}{x+5}\times (x+5)
\\
\\3+\frac{x+5}{5}=2$

Multiply all terms by 5 to eliminate the fraction:

$3\times 5+\frac{x+5}{5}\times 5=2\times 5
\\
\\15+x+5=10$

Combine like terms:

20+x = 10

Subtract 20 from each side:

20+x-20 = 10-20

x = -10

Since this is not -5, this is not an extraneous solution.

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