What is (a/3-b/5)(3/a-5/b) ?

The solution to (a/3-b/5)(3/a-5/b) is -((5a-3b)^2)/(15ab)

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simplify (a/3-b/5)(3/a-5/b)

simplify

(\frac{a}{3} - \frac{b}{5}) (\frac{3}{a} - \frac{5}{b})

- \frac{( 5 a - 3 b ) ^{2}}{15 ab}

Solution steps

(\frac{a}{3} - \frac{b}{5}) (\frac{3}{a} - \frac{5}{b})

Simplify

\frac{a}{3} - \frac{b}{5} : \frac{5 a - 3 b}{15}

= \frac{5 a - 3 b}{15} (\frac{3}{a} - \frac{5}{b})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 5 a - 3 b ) ( \frac{3}{a} - \frac{5}{b} )}{15}

Simplify

(5 a - 3 b) (\frac{3}{a} - \frac{5}{b}) : \frac{( 5 a - 3 b ) ( 3 b - 5 a )}{ab}

= \frac{\frac{( 5 a - 3 b ) ( 3 b - 5 a )}{ab}}{15}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{( 5 a - 3 b ) ( 3 b - 5 a )}{ab \cdot 15}

Simplify

(5 a - 3 b) (3 b - 5 a) : - (5 a - 3 b)^{2}

= \frac{- ( 5 a - 3 b ) ^{2}}{ab \cdot 15}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{( 5 a - 3 b ) ^{2}}{ab \cdot 15}

= - \frac{( 5 a - 3 b ) ^{2}}{15 ab}

- 3 x^{2} - 16 x - 75

(2 a^{2} - b)^{3}

(1 - x)^{- 2} - (1 - x)^{\frac{1}{2}}

2 x + x (x - 2) 6 + x (x - 2) (x - 4)

\frac{1}{m} + \frac{1}{n}

What is (a/3-b/5)(3/a-5/b) ?
The solution to (a/3-b/5)(3/a-5/b) is -((5a-3b)^2)/(15ab)