Basic Math Examples

$\frac{4 y - 3}{y + p} = 2$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

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

$y + p, 1$

Step 1.2

Remove parentheses.

$y + p, 1$

Step 1.3

The LCM of one and any expression is the expression.

$y + p$

Step 2

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

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Step 2.1

Multiply each term in $\frac{4 y - 3}{y + p} = 2$ by $y + p$ .

$\frac{4 y - 3}{y + p} (y + p) = 2 (y + p)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $y + p$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 y - 3}{y + p} (y + p) = 2 (y + p)$

Step 2.2.1.2

Rewrite the expression.

$4 y - 3 = 2 (y + p)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$4 y - 3 = 2 y + 2 p$

Step 3

Solve the equation.

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Step 3.1

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

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Step 3.1.1

Subtract $2 y$ from both sides of the equation.

$4 y - 3 - 2 y = 2 p$

Step 3.1.2

Subtract $2 y$ from $4 y$ .

$2 y - 3 = 2 p$

Step 3.2

Add $3$ to both sides of the equation.

$2 y = 2 p + 3$

Step 3.3

Divide each term in $2 y = 2 p + 3$ by $2$ and simplify.

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Step 3.3.1

Divide each term in $2 y = 2 p + 3$ by $2$ .

$\frac{2 y}{2} = \frac{2 p}{2} + \frac{3}{2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{2 p}{2} + \frac{3}{2}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{2 p}{2} + \frac{3}{2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Cancel the common factor of $2$ .

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Step 3.3.3.1.1

Cancel the common factor.

$y = \frac{2 p}{2} + \frac{3}{2}$

Step 3.3.3.1.2

Divide $p$ by $1$ .

$y = p + \frac{3}{2}$