Simplify x-5*7/(x^3-5x^2)

$x - 5 \cdot \frac{7}{x^{3} - 5 x^{2}}$

Simplify each term.

Factor $x^{2}$ out of $x^{3} - 5 x^{2}$ .

Factor $x^{2}$ out of $x^{3}$ .

$x - 5 \cdot \frac{7}{x^{2} x - 5 x^{2}}$

Factor $x^{2}$ out of $- 5 x^{2}$ .

$x - 5 \cdot \frac{7}{x^{2} x + x^{2} \cdot - 5}$

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot - 5$ .

$x - 5 \cdot \frac{7}{x^{2} (x - 5)}$

Multiply $- 5 \frac{7}{x^{2} (x - 5)}$ .

Combine $- 5$ and $\frac{7}{x^{2} (x - 5)}$ .

$x + \frac{- 5 \cdot 7}{x^{2} (x - 5)}$

Multiply $- 5$ by $7$ .

$x + \frac{- 35}{x^{2} (x - 5)}$

Move the negative in front of the fraction.

$x - \frac{35}{x^{2} (x - 5)}$

To write $x$ as a fraction with a common denominator, multiply by $\frac{(x - 5) x^{2}}{(x - 5) x^{2}}$ .

$x \cdot \frac{(x - 5) x^{2}}{(x - 5) x^{2}} - \frac{35}{x^{2} (x - 5)}$

Write each expression with a common denominator of $(x - 5) x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Combine $x$ and $\frac{(x - 5) x^{2}}{(x - 5) x^{2}}$ .

$\frac{x ((x - 5) x^{2})}{(x - 5) x^{2}} - \frac{35}{x^{2} (x - 5)}$

Reorder the factors of $(x - 5) x^{2}$ .

$\frac{x ((x - 5) x^{2})}{x^{2} (x - 5)} - \frac{35}{x^{2} (x - 5)}$

Combine the numerators over the common denominator.

$\frac{x ((x - 5) x^{2}) - 35}{x^{2} (x - 5)}$

Simplify the numerator.

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{x^{2} x (x - 5) - 35}{x^{2} (x - 5)}$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{x^{2} x^{1} (x - 5) - 35}{x^{2} (x - 5)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{2 + 1} (x - 5) - 35}{x^{2} (x - 5)}$

Add $2$ and $1$ .

$\frac{x^{3} (x - 5) - 35}{x^{2} (x - 5)}$

Apply the distributive property.

$\frac{x^{3} x + x^{3} \cdot - 5 - 35}{x^{2} (x - 5)}$

Multiply $x^{3}$ by $x$ by adding the exponents.

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{x^{3} x^{1} + x^{3} \cdot - 5 - 35}{x^{2} (x - 5)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{3 + 1} + x^{3} \cdot - 5 - 35}{x^{2} (x - 5)}$

Add $3$ and $1$ .

$\frac{x^{4} + x^{3} \cdot - 5 - 35}{x^{2} (x - 5)}$

Move $- 5$ to the left of $x^{3}$ .

$\frac{x^{4} - 5 x^{3} - 35}{x^{2} (x - 5)}$

Simplify x-5*7/(x^3-5x^2)

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