What is expand ((-6/5 x^3y^2))/((3/5 x^2y^2)) ?

The solution to expand ((-6/5 x^3y^2))/((3/5 x^2y^2)) is -2x

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expand ((-6/5 x^3y^2))/((3/5 x^2y^2))

expand

\frac{( - \frac{6}{5} x ^{3} y ^{2} )}{( \frac{3}{5} x ^{2} y ^{2} )}

- 2 x

Solution steps

\frac{- \frac{6}{5} x ^{3} y ^{2}}{\frac{3}{5} x ^{2} y ^{2}}

Apply the fraction rule:

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

= - \frac{\frac{6}{5} x ^{3} y ^{2}}{\frac{3}{5} x ^{2} y ^{2}}

Multiply

\frac{6}{5} x^{3} y^{2} : \frac{6 x ^{3} y ^{2}}{5}

= - \frac{\frac{6 x ^{3} y ^{2}}{5}}{\frac{3}{5} x ^{2} y ^{2}}

Apply the fraction rule:

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

= - \frac{6 x ^{3} y ^{2}}{5 \cdot \frac{3}{5} x ^{2} y ^{2}}

Multiply

5 \cdot \frac{3}{5} x^{2} y^{2} : 3 x^{2} y^{2}

= - \frac{6 x ^{3} y ^{2}}{3 x ^{2} y ^{2}}

Divide the numbers:

\frac{6}{3} = 2

= \frac{2 x ^{3} y ^{2}}{x ^{2} y ^{2}}

Apply exponent rule:

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

\frac{x ^{3}}{x ^{2}} = x^{3 - 2}

= \frac{2 y ^{2} x ^{3 - 2}}{y ^{2}}

Subtract the numbers:

3 - 2 = 1

= \frac{2 x y ^{2}}{y ^{2}}

Cancel the common factor:

y^{2}

= - 2 x

e^{t} (H (t) - H (t - 3)) + e^{t - 3} H (t - 3)

(1 + \frac{x}{2})^{7}

(1 + \frac{x}{2})^{3}

(3 - 3 i)^{5}

(3 - t)^{2}

What is expand ((-6/5 x^3y^2))/((3/5 x^2y^2)) ?
The solution to expand ((-6/5 x^3y^2))/((3/5 x^2y^2)) is -2x