Algebra Examples

$g = y + \frac{c}{x}$

Step 1

Rewrite the equation as $y + \frac{c}{x} = g$ .

$y + \frac{c}{x} = g$

Step 2

Subtract $y$ from both sides of the equation.

$\frac{c}{x} = g - y$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

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

$x, 1, 1$

Step 3.2

The LCM of one and any expression is the expression.

$x$

Step 4

Multiply each term in $\frac{c}{x} = g - y$ by $x$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{c}{x} = g - y$ by $x$ .

$\frac{c}{x} x = g x - y x$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{c}{x} x = g x - y x$

Step 4.2.1.2

Rewrite the expression.

$c = g x - y x$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $g x - y x = c$ .

$g x - y x = c$

Step 5.2

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

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Step 5.2.1

Factor $x$ out of $g x$ .

$x g - y x = c$

Step 5.2.2

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

$x g + x (- y) = c$

Step 5.2.3

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

$x (g - y) = c$

Step 5.3

Divide each term in $x (g - y) = c$ by $g - y$ and simplify.

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Step 5.3.1

Divide each term in $x (g - y) = c$ by $g - y$ .

$\frac{x (g - y)}{g - y} = \frac{c}{g - y}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $g - y$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{x (g - y)}{g - y} = \frac{c}{g - y}$

Step 5.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{c}{g - y}$