Solve for A A/(3x)*(3x+3)/(x^2-2x-3)=1

$\frac{A}{3 x} \cdot \frac{3 x + 3}{x^{2} - 2 x - 3} = 1$

Step 1

Multiply $\frac{A}{3 x}$ by $\frac{3 x + 3}{x^{2} - 2 x - 3}$ .

$\frac{A (3 x + 3)}{3 x (x^{2} - 2 x - 3)} = 1$

Step 2

Multiply each term in $\frac{A (3 x + 3)}{3 x (x^{2} - 2 x - 3)} = 1$ by $\frac{x^{2} - 2 x - 3}{3 x + 3}$ to eliminate the fractions.

Multiply each term in $\frac{A (3 x + 3)}{3 x (x^{2} - 2 x - 3)} = 1$ by $\frac{x^{2} - 2 x - 3}{3 x + 3}$ .

$\frac{A (3 x + 3)}{3 x (x^{2} - 2 x - 3)} \cdot \frac{x^{2} - 2 x - 3}{3 x + 3} = 1 \frac{x^{2} - 2 x - 3}{3 x + 3}$

Simplify the left side.

Cancel the common factor of $3 x + 3$ .

Factor $3 x + 3$ out of $A (3 x + 3)$ .

$\frac{(3 x + 3) A}{3 x (x^{2} - 2 x - 3)} \cdot \frac{x^{2} - 2 x - 3}{3 x + 3} = 1 \frac{x^{2} - 2 x - 3}{3 x + 3}$

Cancel the common factor.

$\frac{(3 x + 3) A}{3 x (x^{2} - 2 x - 3)} \cdot \frac{x^{2} - 2 x - 3}{3 x + 3} = 1 \frac{x^{2} - 2 x - 3}{3 x + 3}$

Rewrite the expression.

$\frac{A}{3 x (x^{2} - 2 x - 3)} (x^{2} - 2 x - 3) = 1 \frac{x^{2} - 2 x - 3}{3 x + 3}$

Cancel the common factor of $x^{2} - 2 x - 3$ .

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

$\frac{A}{(x^{2} - 2 x - 3) (3 x)} (x^{2} - 2 x - 3) = 1 \frac{x^{2} - 2 x - 3}{3 x + 3}$

Cancel the common factor.

$\frac{A}{(x^{2} - 2 x - 3) (3 x)} (x^{2} - 2 x - 3) = 1 \frac{x^{2} - 2 x - 3}{3 x + 3}$

Rewrite the expression.

$\frac{A}{3 x} = 1 \frac{x^{2} - 2 x - 3}{3 x + 3}$

Simplify the right side.

Multiply $\frac{x^{2} - 2 x - 3}{3 x + 3}$ by $1$ .

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

Factor $x^{2} - 2 x - 3$ 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 $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Write the factored form using these integers.

$\frac{A}{3 x} = \frac{(x - 3) (x + 1)}{3 x + 3}$

Simplify terms.

Factor $3$ out of $3 x + 3$ .

Factor $3$ out of $3 x$ .

$\frac{A}{3 x} = \frac{(x - 3) (x + 1)}{3 (x) + 3}$

Factor $3$ out of $3$ .

$\frac{A}{3 x} = \frac{(x - 3) (x + 1)}{3 (x) + 3 (1)}$

Factor $3$ out of $3 (x) + 3 (1)$ .

$\frac{A}{3 x} = \frac{(x - 3) (x + 1)}{3 (x + 1)}$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{A}{3 x} = \frac{(x - 3) (x + 1)}{3 (x + 1)}$

Rewrite the expression.

$\frac{A}{3 x} = \frac{x - 3}{3}$

Step 3

Multiply both sides by $3 x$ .

$\frac{A}{3 x} (3 x) = \frac{x - 3}{3} (3 x)$

Step 4

Simplify.

Simplify the left side.

Simplify $\frac{A}{3 x} (3 x)$ .

Rewrite using the commutative property of multiplication.

$3 \frac{A}{3 x} x = \frac{x - 3}{3} (3 x)$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$3 \frac{A}{3 (x)} x = \frac{x - 3}{3} (3 x)$

Cancel the common factor.

$3 \frac{A}{3 x} x = \frac{x - 3}{3} (3 x)$

Rewrite the expression.

$\frac{A}{x} x = \frac{x - 3}{3} (3 x)$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{A}{x} x = \frac{x - 3}{3} (3 x)$

Rewrite the expression.

$A = \frac{x - 3}{3} (3 x)$

Simplify the right side.

Simplify $\frac{x - 3}{3} (3 x)$ .

Rewrite using the commutative property of multiplication.

$A = 3 \frac{x - 3}{3} x$

Cancel the common factor of $3$ .

Cancel the common factor.

$A = 3 \frac{x - 3}{3} x$

Rewrite the expression.

$A = (x - 3) x$

Apply the distributive property.

$A = x \cdot x - 3 x$

Multiply $x$ by $x$ .

$A = x^{2} - 3 x$

Solve for A A/(3x)*(3x+3)/(x^2-2x-3)=1

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