Algebra Examples

$M g (\frac{3 L}{2} - y) = mg y$

Step 1

Simplify $M g (\frac{3 L}{2} - y)$ .

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Step 1.1

Apply the distributive property.

$y = M g \frac{3 L}{2} + M g (- y)$

Step 1.2

Multiply $M g \frac{3 L}{2}$ .

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Step 1.2.1

Combine $M$ and $\frac{3 L}{2}$ .

$y = g \frac{M (3 L)}{2} + M g (- y)$

Step 1.2.2

Combine $g$ and $\frac{M (3 L)}{2}$ .

$y = \frac{g (M (3 L))}{2} + M g (- y)$

Step 1.3

Rewrite using the commutative property of multiplication.

$y = \frac{g (M (3 L))}{2} - M g y$

Step 1.4

Move $3$ to the left of $g M$ .

$y = \frac{3 g M L}{2} - M g y$

Step 2

Add $M g y$ to both sides of the equation.

$y + M g y = \frac{3 g M L}{2}$

Step 3

Factor $y$ out of $y + M g y$ .

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Step 3.1

Factor $y$ out of $y^{1}$ .

$y \cdot 1 + M g y = \frac{3 g M L}{2}$

Step 3.2

Factor $y$ out of $M g y$ .

$y \cdot 1 + y (M g) = \frac{3 g M L}{2}$

Step 3.3

Factor $y$ out of $y \cdot 1 + y (M g)$ .

$y (1 + M g) = \frac{3 g M L}{2}$

Step 4

Divide each term in $y (1 + M g) = \frac{3 g M L}{2}$ by $1 + M g$ and simplify.

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Step 4.1

Divide each term in $y (1 + M g) = \frac{3 g M L}{2}$ by $1 + M g$ .

$\frac{y (1 + M g)}{1 + M g} = \frac{\frac{3 g M L}{2}}{1 + M g}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $1 + M g$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{y (1 + M g)}{1 + M g} = \frac{\frac{3 g M L}{2}}{1 + M g}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{3 g M L}{2}}{1 + M g}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{3 g M L}{2} \cdot \frac{1}{1 + M g}$

Step 4.3.2

Multiply $\frac{3 g M L}{2}$ by $\frac{1}{1 + M g}$ .

$y = \frac{3 g M L}{2 (1 + M g)}$