What is ((b^2-5b))/((3b-4a))*((9b^2-16a^2))/((b^2-25)) ?

The solution to ((b^2-5b))/((3b-4a))*((9b^2-16a^2))/((b^2-25)) is (b(3b+4a))/(b+5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((b^2-5b))/((3b-4a))*((9b^2-16a^2))/((b^2-25))

simplify

\frac{( b ^{2} - 5 b )}{( 3 b - 4 a )} \cdot \frac{( 9 b ^{2} - 16 a ^{2} )}{( b ^{2} - 25 )}

\frac{b ( 3 b + 4 a )}{b + 5}

Solution steps

\frac{b ^{2} - 5 b}{3 b - 4 a} \cdot \frac{9 b ^{2} - 16 a ^{2}}{b ^{2} - 25}

Apply the fraction rule:

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

= \frac{( b ^{2} - 5 b ) ( 9 b ^{2} - 16 a ^{2} )}{( 3 b - 4 a ) ( b ^{2} - 25 )}

Factor

9 b^{2} - 16 a^{2} : (3 b + 4 a) (3 b - 4 a)

= \frac{( b ^{2} - 5 b ) ( 3 b + 4 a ) ( 3 b - 4 a )}{( 3 b - 4 a ) ( b ^{2} - 25 )}

Cancel the common factor:

3 b - 4 a

= \frac{( b ^{2} - 5 b ) ( 3 b + 4 a )}{b ^{2} - 25}

Factor

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

= \frac{b ( b - 5 ) ( 3 b + 4 a )}{b ^{2} - 25}

Factor

b^{2} - 25 : (b + 5) (b - 5)

= \frac{b ( b - 5 ) ( 3 b + 4 a )}{( b + 5 ) ( b - 5 )}

Cancel the common factor:

b - 5

= \frac{b ( 3 b + 4 a )}{b + 5}

(\frac{x}{3} - \frac{y}{2})^{3}

(\frac{x ^{4} + 1}{x ^{4}}) (\frac{x + 1}{x})

2 x^{4} + x^{3} - 14 x^{2} - 19 x - 6

\frac{1}{2 x y ^{2} ( \frac{2}{3} x y - 3 )}

\frac{1}{2} x + \frac{1}{x}

What is ((b^2-5b))/((3b-4a))*((9b^2-16a^2))/((b^2-25)) ?
The solution to ((b^2-5b))/((3b-4a))*((9b^2-16a^2))/((b^2-25)) is (b(3b+4a))/(b+5)