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Popular >

simplify (a/b+b/a)^2-(a/b-b/a)^2

Solution

simplify

(\frac{a}{b} + \frac{b}{a})^{2} - (\frac{a}{b} - \frac{b}{a})^{2}

Solution

4

Solution steps

(\frac{a}{b} + \frac{b}{a})^{2} - (\frac{a}{b} - \frac{b}{a})^{2}

(\frac{a}{b} + \frac{b}{a})^{2} = \frac{( a ^{2} + b ^{2} ) ^{2}}{a ^{2} b ^{2}}

(\frac{a}{b} - \frac{b}{a})^{2} = \frac{( a ^{2} - b ^{2} ) ^{2}}{a ^{2} b ^{2}}

= \frac{( a ^{2} + b ^{2} ) ^{2}}{a ^{2} b ^{2}} - \frac{( a ^{2} - b ^{2} ) ^{2}}{a ^{2} b ^{2}}

Join

\frac{( a ^{2} + b ^{2} ) ^{2}}{a ^{2} b ^{2}} - \frac{( a ^{2} - b ^{2} ) ^{2}}{a ^{2} b ^{2}} : 4

= 4

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Frequently Asked Questions (FAQ)

What is (a/b+b/a)^2-(a/b-b/a)^2 ?
The solution to (a/b+b/a)^2-(a/b-b/a)^2 is 4