Math

QuestionIdentify the mistake in 1a+1b=1a+b\frac{1}{a}+\frac{1}{b}=\frac{1}{a+b} and correct the right side of the equation.

Studdy Solution

STEP 1

Assumptions1. The variables a and b are real numbers and are not equal to zero.

STEP 2

The error in the equation is in the addition of the fractions. The right side of the equation is incorrectly simplified. The correct way to add fractions is to find a common denominator and then add the numerators.

STEP 3

The correct way to add 1a\frac{1}{a} and 1b\frac{1}{b} is to find a common denominator. The common denominator of 1a\frac{1}{a} and 1b\frac{1}{b} is abab.

STEP 4

After finding the common denominator, we rewrite each fraction as an equivalent fraction with the common denominator.
1a=bab\frac{1}{a} = \frac{b}{ab}1b=aab\frac{1}{b} = \frac{a}{ab}

STEP 5

Now we can add the two fractions.
bab+aab=b+aab\frac{b}{ab} + \frac{a}{ab} = \frac{b+a}{ab}

STEP 6

So the correct equation should be1a+1b=b+aab\frac{1}{a} + \frac{1}{b} = \frac{b+a}{ab}

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