Solve for w (w^2-10)/(w+2)+w-4=w-3

$\frac{w^{2} - 10}{w + 2} + w - 4 = w - 3$

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$w + 2, 1, 1, 1, 1$

Remove parentheses.

$w + 2, 1, 1, 1, 1$

The LCM of one and any expression is the expression.

$w + 2$

Step 2

Multiply each term in $\frac{w^{2} - 10}{w + 2} + w - 4 = w - 3$ by $w + 2$ to eliminate the fractions.

Multiply each term in $\frac{w^{2} - 10}{w + 2} + w - 4 = w - 3$ by $w + 2$ .

$\frac{w^{2} - 10}{w + 2} (w + 2) + w (w + 2) - 4 (w + 2) = w (w + 2) - 3 (w + 2)$

Simplify the left side.

Simplify each term.

Cancel the common factor of $w + 2$ .

Cancel the common factor.

$\frac{w^{2} - 10}{w + 2} (w + 2) + w (w + 2) - 4 (w + 2) = w (w + 2) - 3 (w + 2)$

Rewrite the expression.

$w^{2} - 10 + w (w + 2) - 4 (w + 2) = w (w + 2) - 3 (w + 2)$

Apply the distributive property.

$w^{2} - 10 + w \cdot w + w \cdot 2 - 4 (w + 2) = w (w + 2) - 3 (w + 2)$

Multiply $w$ by $w$ .

$w^{2} - 10 + w^{2} + w \cdot 2 - 4 (w + 2) = w (w + 2) - 3 (w + 2)$

Move $2$ to the left of $w$ .

$w^{2} - 10 + w^{2} + 2 \cdot w - 4 (w + 2) = w (w + 2) - 3 (w + 2)$

Apply the distributive property.

$w^{2} - 10 + w^{2} + 2 w - 4 w - 4 \cdot 2 = w (w + 2) - 3 (w + 2)$

Multiply $- 4$ by $2$ .

$w^{2} - 10 + w^{2} + 2 w - 4 w - 8 = w (w + 2) - 3 (w + 2)$

Simplify by adding terms.

Add $w^{2}$ and $w^{2}$ .

$2 w^{2} - 10 + 2 w - 4 w - 8 = w (w + 2) - 3 (w + 2)$

Subtract $8$ from $- 10$ .

$2 w^{2} + 2 w - 4 w - 18 = w (w + 2) - 3 (w + 2)$

Subtract $4 w$ from $2 w$ .

$2 w^{2} - 2 w - 18 = w (w + 2) - 3 (w + 2)$

Simplify the right side.

Simplify each term.

Apply the distributive property.

$2 w^{2} - 2 w - 18 = w \cdot w + w \cdot 2 - 3 (w + 2)$

Multiply $w$ by $w$ .

$2 w^{2} - 2 w - 18 = w^{2} + w \cdot 2 - 3 (w + 2)$

Move $2$ to the left of $w$ .

$2 w^{2} - 2 w - 18 = w^{2} + 2 \cdot w - 3 (w + 2)$

Apply the distributive property.

$2 w^{2} - 2 w - 18 = w^{2} + 2 w - 3 w - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$2 w^{2} - 2 w - 18 = w^{2} + 2 w - 3 w - 6$

Subtract $3 w$ from $2 w$ .

$2 w^{2} - 2 w - 18 = w^{2} - w - 6$

Step 3

Solve the equation.

Move all terms containing $w$ to the left side of the equation.

Subtract $w^{2}$ from both sides of the equation.

$2 w^{2} - 2 w - 18 - w^{2} = - w - 6$

Add $w$ to both sides of the equation.

$2 w^{2} - 2 w - 18 - w^{2} + w = - 6$

Subtract $w^{2}$ from $2 w^{2}$ .

$w^{2} - 2 w - 18 + w = - 6$

Add $- 2 w$ and $w$ .

$w^{2} - w - 18 = - 6$

Add $6$ to both sides of the equation.

$w^{2} - w - 18 + 6 = 0$

Add $- 18$ and $6$ .

$w^{2} - w - 12 = 0$

Factor $w^{2} - w - 12$ 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 $- 12$ and whose sum is $- 1$ .

$- 4, 3$

Write the factored form using these integers.

$(w - 4) (w + 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$w - 4 = 0$

$w + 3 = 0$

Set $w - 4$ equal to $0$ and solve for $w$ .

Set $w - 4$ equal to $0$ .

$w - 4 = 0$

Add $4$ to both sides of the equation.

$w = 4$

Set $w + 3$ equal to $0$ and solve for $w$ .

Set $w + 3$ equal to $0$ .

$w + 3 = 0$

Subtract $3$ from both sides of the equation.

$w = - 3$

The final solution is all the values that make $(w - 4) (w + 3) = 0$ true.

$w = 4, - 3$

Solve for w (w^2-10)/(w+2)+w-4=w-3

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