What is (3b-5)/(b^2)*(b^4)/(5-3b) ?

The solution to (3b-5)/(b^2)*(b^4)/(5-3b) is -b^2

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simplify (3b-5)/(b^2)*(b^4)/(5-3b)

simplify

\frac{3 b - 5}{b ^{2}} \cdot \frac{b ^{4}}{5 - 3 b}

- b^{2}

Solution steps

\frac{3 b - 5}{b ^{2}} \cdot \frac{b ^{4}}{5 - 3 b}

Apply the fraction rule:

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

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

b^{4} = b^{2} b^{2}

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

Cancel the common factor:

b^{2}

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

5 - 3 b = - (3 b - 5)

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

Cancel the common factor:

3 b - 5

= \frac{b ^{2}}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - b^{2}

4 y^{2}

5 a^{2} - 8 a + 3

4 (x - 2)^{2}

\frac{9 a + 9}{a ^{2} + 2 a + 1}

\frac{1}{8} + \frac{6}{8}

What is (3b-5)/(b^2)*(b^4)/(5-3b) ?
The solution to (3b-5)/(b^2)*(b^4)/(5-3b) is -b^2