Basic Math Examples

\frac{y}{7 y - 2} = \frac{3 y}{13 y - 4}

$\frac{y}{7 y - 2} = \frac{3 y}{13 y - 4}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

y (13 y - 4) = (7 y - 2) (3 y)

$y (13 y - 4) = (7 y - 2) (3 y)$

Step 2

Solve the equation for

y

$y$ .

Tap for more steps...

Step 2.1

Simplify

y (13 y - 4)

$y (13 y - 4)$ .

Tap for more steps...

Step 2.1.1

Rewrite.

0 + 0 + y (13 y - 4) = (7 y - 2) \cdot (3 y)

$0 + 0 + y (13 y - 4) = (7 y - 2) \cdot (3 y)$

Step 2.1.2

Simplify by multiplying through.

Tap for more steps...

Step 2.1.2.1

Apply the distributive property.

y (13 y) + y \cdot - 4 = (7 y - 2) \cdot (3 y)

$y (13 y) + y \cdot - 4 = (7 y - 2) \cdot (3 y)$

Step 2.1.2.2

Reorder.

Tap for more steps...

Step 2.1.2.2.1

Rewrite using the commutative property of multiplication.

13 y \cdot y + y \cdot - 4 = (7 y - 2) \cdot (3 y)

$13 y \cdot y + y \cdot - 4 = (7 y - 2) \cdot (3 y)$

Step 2.1.2.2.2

Move

- 4

$- 4$ to the left of

y

$y$ .

13 y \cdot y - 4 \cdot y = (7 y - 2) \cdot (3 y)

$13 y \cdot y - 4 \cdot y = (7 y - 2) \cdot (3 y)$

13 y \cdot y - 4 \cdot y = (7 y - 2) \cdot (3 y)

$13 y \cdot y - 4 \cdot y = (7 y - 2) \cdot (3 y)$

13 y \cdot y - 4 \cdot y = (7 y - 2) \cdot (3 y)

$13 y \cdot y - 4 \cdot y = (7 y - 2) \cdot (3 y)$

Step 2.1.3

Multiply

y

$y$ by

y

$y$ by adding the exponents.

Tap for more steps...

Step 2.1.3.1

Move

y

$y$ .

13 (y \cdot y) - 4 \cdot y = (7 y - 2) \cdot (3 y)

$13 (y \cdot y) - 4 \cdot y = (7 y - 2) \cdot (3 y)$

Step 2.1.3.2

Multiply

y

$y$ by

y

$y$ .

13 y^{2} - 4 \cdot y = (7 y - 2) \cdot (3 y)

$13 y^{2} - 4 \cdot y = (7 y - 2) \cdot (3 y)$

13 y^{2} - 4 y = (7 y - 2) \cdot (3 y)

$13 y^{2} - 4 y = (7 y - 2) \cdot (3 y)$

13 y^{2} - 4 y = (7 y - 2) \cdot (3 y)

$13 y^{2} - 4 y = (7 y - 2) \cdot (3 y)$

Step 2.2

Simplify

(7 y - 2) \cdot (3 y)

$(7 y - 2) \cdot (3 y)$ .

Tap for more steps...

Step 2.2.1

Simplify by multiplying through.

Tap for more steps...

Step 2.2.1.1

Apply the distributive property.

13 y^{2} - 4 y = 7 y (3 y) - 2 (3 y)

$13 y^{2} - 4 y = 7 y (3 y) - 2 (3 y)$

Step 2.2.1.2

Simplify the expression.

Tap for more steps...

Step 2.2.1.2.1

Rewrite using the commutative property of multiplication.

13 y^{2} - 4 y = 7 \cdot 3 y \cdot y - 2 (3 y)

$13 y^{2} - 4 y = 7 \cdot 3 y \cdot y - 2 (3 y)$

Step 2.2.1.2.2

Multiply

3

$3$ by

- 2

$- 2$ .

13 y^{2} - 4 y = 7 \cdot 3 y \cdot y - 6 y

$13 y^{2} - 4 y = 7 \cdot 3 y \cdot y - 6 y$

13 y^{2} - 4 y = 7 \cdot 3 y \cdot y - 6 y

$13 y^{2} - 4 y = 7 \cdot 3 y \cdot y - 6 y$

13 y^{2} - 4 y = 7 \cdot 3 y \cdot y - 6 y

$13 y^{2} - 4 y = 7 \cdot 3 y \cdot y - 6 y$

Step 2.2.2

Simplify each term.

Tap for more steps...

Step 2.2.2.1

Multiply

y

$y$ by

y

$y$ by adding the exponents.

Tap for more steps...

Step 2.2.2.1.1

Move

y

$y$ .

13 y^{2} - 4 y = 7 \cdot 3 (y \cdot y) - 6 y

$13 y^{2} - 4 y = 7 \cdot 3 (y \cdot y) - 6 y$

Step 2.2.2.1.2

Multiply

y

$y$ by

y

$y$ .

13 y^{2} - 4 y = 7 \cdot 3 y^{2} - 6 y

$13 y^{2} - 4 y = 7 \cdot 3 y^{2} - 6 y$

13 y^{2} - 4 y = 7 \cdot 3 y^{2} - 6 y

$13 y^{2} - 4 y = 7 \cdot 3 y^{2} - 6 y$

Step 2.2.2.2

Multiply

7

$7$ by

3

$3$ .

13 y^{2} - 4 y = 21 y^{2} - 6 y

$13 y^{2} - 4 y = 21 y^{2} - 6 y$

13 y^{2} - 4 y = 21 y^{2} - 6 y

$13 y^{2} - 4 y = 21 y^{2} - 6 y$

13 y^{2} - 4 y = 21 y^{2} - 6 y

$13 y^{2} - 4 y = 21 y^{2} - 6 y$

Step 2.3

Move all terms containing

y

$y$ to the left side of the equation.

Tap for more steps...

Step 2.3.1

Subtract

21 y^{2}

$21 y^{2}$ from both sides of the equation.

13 y^{2} - 4 y - 21 y^{2} = - 6 y

$13 y^{2} - 4 y - 21 y^{2} = - 6 y$

Step 2.3.2

Add

6 y

$6 y$ to both sides of the equation.

13 y^{2} - 4 y - 21 y^{2} + 6 y = 0

$13 y^{2} - 4 y - 21 y^{2} + 6 y = 0$

Step 2.3.3

Subtract

21 y^{2}

$21 y^{2}$ from

13 y^{2}

$13 y^{2}$ .

- 8 y^{2} - 4 y + 6 y = 0

$- 8 y^{2} - 4 y + 6 y = 0$

Step 2.3.4

Add

- 4 y

$- 4 y$ and

6 y

$6 y$ .

- 8 y^{2} + 2 y = 0

$- 8 y^{2} + 2 y = 0$

- 8 y^{2} + 2 y = 0

$- 8 y^{2} + 2 y = 0$

Step 2.4

Factor

- 2 y

$- 2 y$ out of

- 8 y^{2} + 2 y

$- 8 y^{2} + 2 y$ .

Tap for more steps...

Step 2.4.1

Factor

- 2 y

$- 2 y$ out of

- 8 y^{2}

$- 8 y^{2}$ .

- 2 y (4 y) + 2 y = 0

$- 2 y (4 y) + 2 y = 0$

Step 2.4.2

Factor

- 2 y

$- 2 y$ out of

2 y

$2 y$ .

- 2 y (4 y) - 2 y \cdot - 1 = 0

$- 2 y (4 y) - 2 y \cdot - 1 = 0$

Step 2.4.3

Factor

- 2 y

$- 2 y$ out of

- 2 y (4 y) - 2 y (- 1)

$- 2 y (4 y) - 2 y (- 1)$ .

- 2 y (4 y - 1) = 0

$- 2 y (4 y - 1) = 0$

- 2 y (4 y - 1) = 0

$- 2 y (4 y - 1) = 0$

Step 2.5

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

y = 0

$y = 0$

4 y - 1 = 0

$4 y - 1 = 0$

Step 2.6

Set

y

$y$ equal to

0

$0$ .

y = 0

$y = 0$

Step 2.7

Set

4 y - 1

$4 y - 1$ equal to

0

$0$ and solve for

y

$y$ .

Tap for more steps...

Step 2.7.1

Set

4 y - 1

$4 y - 1$ equal to

0

$0$ .

4 y - 1 = 0

$4 y - 1 = 0$

Step 2.7.2

Solve

4 y - 1 = 0

$4 y - 1 = 0$ for

y

$y$ .

Tap for more steps...

Step 2.7.2.1

Add

1

$1$ to both sides of the equation.

4 y = 1

$4 y = 1$

Step 2.7.2.2

Divide each term in

4 y = 1

$4 y = 1$ by

4

$4$ and simplify.

Tap for more steps...

Step 2.7.2.2.1

Divide each term in

4 y = 1

$4 y = 1$ by

4

$4$ .

\frac{4 y}{4} = \frac{1}{4}

$\frac{4 y}{4} = \frac{1}{4}$

Step 2.7.2.2.2

Simplify the left side.

Tap for more steps...

Step 2.7.2.2.2.1

Cancel the common factor of

4

$4$ .

Tap for more steps...

Step 2.7.2.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{1}{4}$

Step 2.7.2.2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{1}{4}$

Step 2.8

The final solution is all the values that make

$- 2 y (4 y - 1) = 0$ true.

$y = 0, \frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = 0, \frac{1}{4}$

Decimal Form:

$y = 0, 0.25$