Finite Math Examples

$\frac{3 y}{3 + y} + \frac{y}{3 + y} = 4$

Step 1

Subtract $4$ from both sides of the equation.

$\frac{3 y}{3 + y} + \frac{y}{3 + y} - 4 = 0$

Step 2

Simplify $\frac{3 y}{3 + y} + \frac{y}{3 + y} - 4$ .

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Step 2.1

Combine the numerators over the common denominator.

$- 4 + \frac{3 y + y}{y + 3} = 0$

Step 2.2

Add $3 y$ and $y$ .

$- 4 + \frac{4 y}{y + 3} = 0$

Step 2.3

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{y + 3}{y + 3}$ .

$- 4 \cdot \frac{y + 3}{y + 3} + \frac{4 y}{y + 3} = 0$

Step 2.4

Combine $- 4$ and $\frac{y + 3}{y + 3}$ .

$\frac{- 4 (y + 3)}{y + 3} + \frac{4 y}{y + 3} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 4 (y + 3) + 4 y}{y + 3} = 0$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Factor $4$ out of $- 4 (y + 3) + 4 y$ .

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Step 2.6.1.1

Factor $4$ out of $- 4 (y + 3)$ .

$\frac{4 (- (y + 3)) + 4 y}{y + 3} = 0$

Step 2.6.1.2

Factor $4$ out of $4 y$ .

$\frac{4 (- (y + 3)) + 4 (y)}{y + 3} = 0$

Step 2.6.1.3

Factor $4$ out of $4 (- (y + 3)) + 4 (y)$ .

$\frac{4 (- (y + 3) + y)}{y + 3} = 0$

Step 2.6.2

Apply the distributive property.

$\frac{4 (- y - 1 \cdot 3 + y)}{y + 3} = 0$

Step 2.6.3

Multiply $- 1$ by $3$ .

$\frac{4 (- y - 3 + y)}{y + 3} = 0$

Step 2.6.4

Add $- y$ and $y$ .

$\frac{4 (0 - 3)}{y + 3} = 0$

Step 2.6.5

Subtract $3$ from $0$ .

$\frac{4 \cdot - 3}{y + 3} = 0$

Step 2.7

Multiply $4$ by $- 3$ .

$\frac{- 12}{y + 3} = 0$

Step 2.8

Move the negative in front of the fraction.

$- \frac{12}{y + 3} = 0$

Step 3

Set the numerator equal to zero.

$12 = 0$

Step 4

Since $12 \neq 0$ , there are no solutions.

No solution