Divide ((x^2+5x-6)/(10x))÷(x-1)

$\frac{x^{2} + 5 x - 6}{10 x} \div (x - 1)$

Rewrite the division as a fraction.

$\frac{\frac{x^{2} + 5 x - 6}{10 x}}{x - 1}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} + 5 x - 6}{10 x} \cdot \frac{1}{x - 1}$

Factor $x^{2} + 5 x - 6$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $5$ .

$- 1, 6$

Write the factored form using these integers.

$\frac{(x - 1) (x + 6)}{10 x} \cdot \frac{1}{x - 1}$

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{(x - 1) (x + 6)}{10 x} \cdot \frac{1}{x - 1}$

Rewrite the expression.

$\frac{x + 6}{10 x}$

Split the fraction $\frac{x + 6}{10 x}$ into two fractions.

$\frac{x}{10 x} + \frac{6}{10 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x}{10 x} + \frac{6}{10 x}$

Rewrite the expression.

$\frac{1}{10} + \frac{6}{10 x}$

Cancel the common factor of $6$ and $10$ .

Factor $2$ out of $6$ .

$\frac{1}{10} + \frac{2 (3)}{10 x}$

Cancel the common factors.

Factor $2$ out of $10 x$ .

$\frac{1}{10} + \frac{2 (3)}{2 (5 x)}$

Cancel the common factor.

$\frac{1}{10} + \frac{2 \cdot 3}{2 (5 x)}$

Rewrite the expression.

$\frac{1}{10} + \frac{3}{5 x}$

Divide ((x^2+5x-6)/(10x))÷(x-1)

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