Algebra Examples

$- x y - 4 x + 10 y + 3 = 0$

Step 1

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

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Step 1.1

Add $4 x$ to both sides of the equation.

$- x y + 10 y + 3 = 4 x$

Step 1.2

Subtract $3$ from both sides of the equation.

$- x y + 10 y = 4 x - 3$

Step 2

Factor $y$ out of $- x y + 10 y$ .

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Step 2.1

Factor $y$ out of $- x y$ .

$y (- x) + 10 y = 4 x - 3$

Step 2.2

Factor $y$ out of $10 y$ .

$y (- x) + y \cdot 10 = 4 x - 3$

Step 2.3

Factor $y$ out of $y (- x) + y \cdot 10$ .

$y (- x + 10) = 4 x - 3$

Step 3

Divide each term in $y (- x + 10) = 4 x - 3$ by $- x + 10$ and simplify.

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Step 3.1

Divide each term in $y (- x + 10) = 4 x - 3$ by $- x + 10$ .

$\frac{y (- x + 10)}{- x + 10} = \frac{4 x}{- x + 10} + \frac{- 3}{- x + 10}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- x + 10$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{y (- x + 10)}{- x + 10} = \frac{4 x}{- x + 10} + \frac{- 3}{- x + 10}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{4 x}{- x + 10} + \frac{- 3}{- x + 10}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Combine the numerators over the common denominator.

$y = \frac{4 x - 3}{- x + 10}$

Step 3.3.2

Factor $- 1$ out of $- x$ .

$y = \frac{4 x - 3}{- (x) + 10}$

Step 3.3.3

Rewrite $10$ as $- 1 (- 10)$ .

$y = \frac{4 x - 3}{- (x) - 1 (- 10)}$

Step 3.3.4

Factor $- 1$ out of $- (x) - 1 (- 10)$ .

$y = \frac{4 x - 3}{- (x - 10)}$

Step 3.3.5

Rewrite negatives.

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Step 3.3.5.1

Rewrite $- (x - 10)$ as $- 1 (x - 10)$ .

$y = \frac{4 x - 3}{- 1 (x - 10)}$

Step 3.3.5.2

Move the negative in front of the fraction.

$y = - \frac{4 x - 3}{x - 10}$

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = - \frac{4 x - 3}{x - 10}$