Basic Math Examples

$\frac{2 y - 1}{y} = 2$

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.

$y, 1$

Step 1.2

The LCM of one and any expression is the expression.

$y$

Step 2

Multiply each term in $\frac{2 y - 1}{y} = 2$ by $y$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2 y - 1}{y} = 2$ by $y$ .

$\frac{2 y - 1}{y} y = 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $y$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 y - 1}{y} y = 2 y$

Step 2.2.1.2

Rewrite the expression.

$2 y - 1 = 2 y$

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.

$2 y - 1 - 2 y = 0$

Step 3.1.2

Combine the opposite terms in $2 y - 1 - 2 y$ .

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Step 3.1.2.1

Subtract $2 y$ from $2 y$ .

$0 - 1 = 0$

Step 3.1.2.2

Subtract $1$ from $0$ .

$- 1 = 0$

Step 3.2

Since $- 1 \neq 0$ , there are no solutions.

No solution