Solve for D 2x^2D-5y+1=4x+2y^2D

$2 x^{2} D - 5 y + 1 = 4 x + 2 y^{2} D$

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

$2 x^{2} D - 5 y + 1 - 2 y^{2} D = 4 x$

Move all terms not containing $D$ to the right side of the equation.

Add $5 y$ to both sides of the equation.

$2 x^{2} D + 1 - 2 y^{2} D = 4 x + 5 y$

Subtract $1$ from both sides of the equation.

$2 x^{2} D - 2 y^{2} D = 4 x + 5 y - 1$

Factor $2 D$ out of $2 x^{2} D - 2 y^{2} D$ .

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

$2 D (x^{2}) - 2 y^{2} D = 4 x + 5 y - 1$

Factor $2 D$ out of $- 2 y^{2} D$ .

$2 D (x^{2}) + 2 D (- y^{2}) = 4 x + 5 y - 1$

Factor $2 D$ out of $2 D (x^{2}) + 2 D (- y^{2})$ .

$2 D (x^{2} - y^{2}) = 4 x + 5 y - 1$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

$2 D ((x + y) (x - y)) = 4 x + 5 y - 1$

Remove unnecessary parentheses.

$2 D (x + y) (x - y) = 4 x + 5 y - 1$

Divide each term in $2 D (x + y) (x - y) = 4 x + 5 y - 1$ by $2 (x + y) (x - y)$ and simplify.

Divide each term in $2 D (x + y) (x - y) = 4 x + 5 y - 1$ by $2 (x + y) (x - y)$ .

$\frac{2 D (x + y) (x - y)}{2 (x + y) (x - y)} = \frac{4 x}{2 (x + y) (x - y)} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 D (x + y) (x - y)}{2 (x + y) (x - y)} = \frac{4 x}{2 (x + y) (x - y)} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Rewrite the expression.

$\frac{(D (x + y)) (x - y)}{(x + y) (x - y)} = \frac{4 x}{2 (x + y) (x - y)} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Cancel the common factor of $x + y$ .

Cancel the common factor.

$\frac{D (x + y) (x - y)}{(x + y) (x - y)} = \frac{4 x}{2 (x + y) (x - y)} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Rewrite the expression.

$\frac{(D) (x - y)}{x - y} = \frac{4 x}{2 (x + y) (x - y)} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Cancel the common factor of $x - y$ .

Cancel the common factor.

$\frac{D (x - y)}{x - y} = \frac{4 x}{2 (x + y) (x - y)} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Divide $D$ by $1$ .

$D = \frac{4 x}{2 (x + y) (x - y)} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x$ .

$D = \frac{2 (2 x)}{2 (x + y) (x - y)} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Cancel the common factors.

Factor $2$ out of $2 (x + y) (x - y)$ .

$D = \frac{2 (2 x)}{2 ((x + y) (x - y))} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Cancel the common factor.

$D = \frac{2 (2 x)}{2 ((x + y) (x - y))} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Rewrite the expression.

$D = \frac{2 x}{(x + y) (x - y)} + \frac{5 y}{2 (x + y) (x - y)} + \frac{- 1}{2 (x + y) (x - y)}$

Move the negative in front of the fraction.

$D = \frac{2 x}{(x + y) (x - y)} + \frac{5 y}{2 (x + y) (x - y)} - \frac{1}{2 (x + y) (x - y)}$

Solve for D 2x^2D-5y+1=4x+2y^2D

Related Questions

Support LCMGCF.com by disabling your adblocker.