Question

Subtract. (5)/(12wy^(2))-(2)/(9w^(2)y) Simplify your answer as much as possible.

Answer 1

The simplified result of subtracting
`\((5)/(12wy^2)\) from \((2)/(9w^2y)\) is \((1)/(36w^2y)\).`

Step-by-step explanation

To subtract fractions, we need a common denominator. The common denominator here is
`\(36w^2y\)` since it's the least common multiple of the denominators
`\(12wy^2\) and \(9w^2y\).` To make both fractions have this denominator, we'll adjust them accordingly.

For
`\((5)/(12wy^2)\)`, to make the denominator
`\(36w^2y\)`, we need to multiply both the numerator and denominator by
`\(3w\) to get \((15w)/(36w^2y)\).`

For
`\((2)/(9w^2y)\),`to make the denominator
`\(36w^2y\),` we multiply both the numerator and denominator by
`\(4y\)` to get
`\((8y)/(36w^2y)\).`

Now that both fractions have the same denominator, we can subtract them:
`\((15w)/(36w^2y) - (8y)/(36w^2y)\)`. This simplifies to
`\((15w - 8y)/(36w^2y)\).`

Further simplification can be done by noticing that there's no common factor between
`\(15w\) and \(8y\)`, so the expression remains as
`\((15w - 8y)/(36w^2y)\),` which is the final answer.