Algebra Examples

$a = \frac{h (a + b)}{2}$

Step 1

Multiply both sides by $2$ .

$a \cdot 2 = \frac{h (a + b)}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Move $2$ to the left of $a$ .

$2 a = \frac{h (a + b)}{2} \cdot 2$

$2 a = \frac{h (a + b)}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{h (a + b)}{2} \cdot 2$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

$2 a = \frac{h (a + b)}{2} \cdot 2$

Step 2.2.1.1.2

Rewrite the expression.

$2 a = h (a + b)$

$2 a = h (a + b)$

Step 2.2.1.2

Apply the distributive property.

$2 a = h a + h b$

Step 2.2.1.3

Simplify with commuting.

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Step 2.2.1.3.1

Reorder $h$ and $a$ .

$2 a = a h + h b$

Step 2.2.1.3.2

Reorder $h$ and $b$ .

$2 a = a h + b h$

$2 a = a h + b h$

$2 a = a h + b h$

$2 a = a h + b h$

$2 a = a h + b h$

Step 3

Solve for $a$ .

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Step 3.1

Subtract $a h$ from both sides of the equation.

$2 a - a h = b h$

Step 3.2

Factor $a$ out of $2 a - a h$ .

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Step 3.2.1

Factor $a$ out of $2 a$ .

$a \cdot 2 - a h = b h$

Step 3.2.2

Factor $a$ out of $- a h$ .

$a \cdot 2 + a (- 1 h) = b h$

Step 3.2.3

Factor $a$ out of $a \cdot 2 + a (- 1 h)$ .

$a (2 - 1 h) = b h$

$a (2 - 1 h) = b h$

Step 3.3

Rewrite $- 1 h$ as $- h$ .

$a (2 - h) = b h$

Step 3.4

Divide each term in $a (2 - h) = b h$ by $2 - h$ and simplify.

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Step 3.4.1

Divide each term in $a (2 - h) = b h$ by $2 - h$ .

$\frac{a (2 - h)}{2 - h} = \frac{b h}{2 - h}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $2 - h$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{a (2 - h)}{2 - h} = \frac{b h}{2 - h}$

Step 3.4.2.1.2

Divide $a$ by $1$ .

$a = \frac{b h}{2 - h}$

$a = \frac{b h}{2 - h}$

$a = \frac{b h}{2 - h}$

$a = \frac{b h}{2 - h}$

$a = \frac{b h}{2 - h}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$