Algebra Examples

$\frac{1 - 2 y}{3 - y} + y = \frac{1}{y + 2}$

Step 1

Simplify $\frac{1 - 2 y}{3 - y} + y$ .

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Step 1.1

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

$\frac{1 - 2 y}{3 - y} + \frac{y (3 - y)}{3 - y} = \frac{1}{y + 2}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{1 - 2 y + y (3 - y)}{3 - y} = \frac{1}{y + 2}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Apply the distributive property.

$\frac{1 - 2 y + y \cdot 3 + y (- y)}{3 - y} = \frac{1}{y + 2}$

Step 1.3.2

Move $3$ to the left of $y$ .

$\frac{1 - 2 y + 3 \cdot y + y (- y)}{3 - y} = \frac{1}{y + 2}$

Step 1.3.3

Rewrite using the commutative property of multiplication.

$\frac{1 - 2 y + 3 \cdot y - y \cdot y}{3 - y} = \frac{1}{y + 2}$

Step 1.3.4

Multiply $y$ by $y$ by adding the exponents.

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Step 1.3.4.1

Move $y$ .

$\frac{1 - 2 y + 3 y - (y \cdot y)}{3 - y} = \frac{1}{y + 2}$

Step 1.3.4.2

Multiply $y$ by $y$ .

$\frac{1 - 2 y + 3 y - y^{2}}{3 - y} = \frac{1}{y + 2}$

Step 1.3.5

Add $- 2 y$ and $3 y$ .

$\frac{1 + y - y^{2}}{3 - y} = \frac{1}{y + 2}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$y \approx - 2.6510934, 0.27389055, 1.37720285$

Step 3