Solve for y (x-6)/(x+3)*y/(x-6)=x-2

$\frac{x - 6}{x + 3} \cdot \frac{y}{x - 6} = x - 2$

Multiply $\frac{x - 6}{x + 3}$ by $\frac{y}{x - 6}$ .

$\frac{(x - 6) y}{(x + 3) (x - 6)} = x - 2$

Multiply each term in $\frac{(x - 6) y}{(x + 3) (x - 6)} = x - 2$ by $\frac{x + 3}{x - 6}$ to eliminate the fractions.

Multiply each term in $\frac{(x - 6) y}{(x + 3) (x - 6)} = x - 2$ by $\frac{x + 3}{x - 6}$ .

$\frac{(x - 6) y}{(x + 3) (x - 6)} \cdot \frac{x + 3}{x - 6} = x \frac{x + 3}{x - 6} - 2 \frac{x + 3}{x - 6}$

Simplify the left side.

Cancel the common factor of $x - 6$ .

Factor $x - 6$ out of $(x - 6) y$ .

$\frac{(x - 6) (y)}{(x + 3) (x - 6)} \cdot \frac{x + 3}{x - 6} = x \frac{x + 3}{x - 6} - 2 \frac{x + 3}{x - 6}$

Cancel the common factor.

$\frac{(x - 6) y}{(x + 3) (x - 6)} \cdot \frac{x + 3}{x - 6} = x \frac{x + 3}{x - 6} - 2 \frac{x + 3}{x - 6}$

Rewrite the expression.

$\frac{y}{(x + 3) (x - 6)} (x + 3) = x \frac{x + 3}{x - 6} - 2 \frac{x + 3}{x - 6}$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{y}{(x + 3) (x - 6)} (x + 3) = x \frac{x + 3}{x - 6} - 2 \frac{x + 3}{x - 6}$

Rewrite the expression.

$\frac{y}{x - 6} = x \frac{x + 3}{x - 6} - 2 \frac{x + 3}{x - 6}$

Simplify the right side.

Simplify terms.

Simplify each term.

Combine $x$ and $\frac{x + 3}{x - 6}$ .

$\frac{y}{x - 6} = \frac{x (x + 3)}{x - 6} - 2 \frac{x + 3}{x - 6}$

Combine $- 2$ and $\frac{x + 3}{x - 6}$ .

$\frac{y}{x - 6} = \frac{x (x + 3)}{x - 6} + \frac{- 2 (x + 3)}{x - 6}$

Move the negative in front of the fraction.

$\frac{y}{x - 6} = \frac{x (x + 3)}{x - 6} - \frac{2 (x + 3)}{x - 6}$

Combine the numerators over the common denominator.

$\frac{y}{x - 6} = \frac{x (x + 3) - 2 (x + 3)}{x - 6}$

Simplify each term.

Apply the distributive property.

$\frac{y}{x - 6} = \frac{x \cdot x + x \cdot 3 - 2 (x + 3)}{x - 6}$

Multiply $x$ by $x$ .

$\frac{y}{x - 6} = \frac{x^{2} + x \cdot 3 - 2 (x + 3)}{x - 6}$

Move $3$ to the left of $x$ .

$\frac{y}{x - 6} = \frac{x^{2} + 3 \cdot x - 2 (x + 3)}{x - 6}$

Apply the distributive property.

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

Multiply $- 2$ by $3$ .

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

Subtract $2 x$ from $3 x$ .

$\frac{y}{x - 6} = \frac{x^{2} + x - 6}{x - 6}$

Factor $x^{2} + x - 6$ 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 $1$ .

$- 2, 3$

Write the factored form using these integers.

$\frac{y}{x - 6} = \frac{(x - 2) (x + 3)}{x - 6}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$y = (x - 2) (x + 3)$

Simplify both sides.

Expand $(x - 2) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$y = x (x + 3) - 2 (x + 3)$

Apply the distributive property.

$y = x \cdot x + x \cdot 3 - 2 (x + 3)$

Apply the distributive property.

$y = x \cdot x + x \cdot 3 - 2 x - 2 \cdot 3$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot 3 - 2 x - 2 \cdot 3$

Move $3$ to the left of $x$ .

$y = x^{2} + 3 \cdot x - 2 x - 2 \cdot 3$

Multiply $- 2$ by $3$ .

$y = x^{2} + 3 x - 2 x - 6$

Subtract $2 x$ from $3 x$ .

$y = x^{2} + x - 6$

Solve for y (x-6)/(x+3)*y/(x-6)=x-2

Related Questions

Support LCMGCF.com by disabling your adblocker.