Simplify. startstart fraction startfraction 16 over a squared endfraction plus startfraction 24 over ab endfraction plus startfraction 9 over b squared endfraction overover startfraction 16 over a squared endfraction minus startfraction 9 over b squared endfraction end endfraction start startfraction startfraction 16 over a squared endfraction plus startfraction 24 over ab endfraction plus startfraction 9 over b squared endfraction overover startfraction 16 over a squared endfraction minus startfraction 9 over b squared endfraction end endfraction equals nothing (simplify your answer.)

(3a + 4b)² / a²b²

Explanation:

This question is difficult to interpret, however the concept being tested in this question is the ability to simplify fractions with variables.

It is a basic rule that only like terms (as denominators) can be added and subtracted from each other, however if you need to add or subtract two fractions with different denominators, it is important to make sure you create a common denominator.

For example, in the beginning, the first fractions are:

16/a² + 24/ab + 9/b²

So it is important to make sure there is a common denominator between all 3 fractions. An easy way of doing this would be to multiply denominators together:

(16b²)/a²b² + (9a²)/a²b² + 24/ab

(9a²+16b²)/a²b² + 24/ab

So now it has gone from 3 fractions to 2, and then to 1:

(9a²+16b²)/a²b² + 24ab/a²b²

(9a² + 24ab + 16b²) / a²b²

Then all that needs to be done is simplify the numerator:

(3a + 4b)² / a²b²

(3a + 4b)² / a²b²

Explanation:

This question is difficult to interpret, however the concept being tested in this question is the ability to simplify fractions with variables.

It is a basic rule that only like terms (as denominators) can be added and subtracted from each other, however if you need to add or subtract two fractions with different denominators, it is important to make sure you create a common denominator.

For example, in the beginning, the first fractions are:

16/a² + 24/ab + 9/b²

So it is important to make sure there is a common denominator between all 3 fractions. An easy way of doing this would be to multiply denominators together:

(16b²)/a²b² + (9a²)/a²b² + 24/ab

(9a²+16b²)/a²b² + 24/ab

So now it has gone from 3 fractions to 2, and then to 1:

(9a²+16b²)/a²b² + 24ab/a²b²

(9a² + 24ab + 16b²) / a²b²

Then all that needs to be done is simplify the numerator:

(3a + 4b)² / a²b²

Explanation:

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explanation: