Algebra Examples

$\frac{8 m^{2} + 5 m - 3}{5 m + 5} = 1$

Step 1

Factor each term.

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Step 1.1

Factor by grouping.

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Step 1.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 8 \cdot - 3 = - 24$ and whose sum is $b = 5$ .

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Step 1.1.1.1

Factor $5$ out of $5 m$ .

$\frac{8 m^{2} + 5 (m) - 3}{5 m + 5} = 1$

Step 1.1.1.2

Rewrite $5$ as $- 3$ plus $8$

$\frac{8 m^{2} + (- 3 + 8) m - 3}{5 m + 5} = 1$

Step 1.1.1.3

Apply the distributive property.

$\frac{8 m^{2} - 3 m + 8 m - 3}{5 m + 5} = 1$

Step 1.1.2

Factor out the greatest common factor from each group.

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Step 1.1.2.1

Group the first two terms and the last two terms.

$\frac{(8 m^{2} - 3 m) + 8 m - 3}{5 m + 5} = 1$

Step 1.1.2.2

Factor out the greatest common factor (GCF) from each group.

$\frac{m (8 m - 3) + 1 (8 m - 3)}{5 m + 5} = 1$

Step 1.1.3

Factor the polynomial by factoring out the greatest common factor, $8 m - 3$ .

$\frac{(8 m - 3) (m + 1)}{5 m + 5} = 1$

Step 1.2

Factor $5$ out of $5 m + 5$ .

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Step 1.2.1

Factor $5$ out of $5 m$ .

$\frac{(8 m - 3) (m + 1)}{5 (m) + 5} = 1$

Step 1.2.2

Factor $5$ out of $5$ .

$\frac{(8 m - 3) (m + 1)}{5 (m) + 5 (1)} = 1$

Step 1.2.3

Factor $5$ out of $5 (m) + 5 (1)$ .

$\frac{(8 m - 3) (m + 1)}{5 (m + 1)} = 1$

Step 1.3

Reduce the expression $\frac{(8 m - 3) (m + 1)}{5 (m + 1)}$ by cancelling the common factors.

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Step 1.3.1

Cancel the common factor.

$\frac{(8 m - 3) (m + 1)}{5 (m + 1)} = 1$

Step 1.3.2

Rewrite the expression.

$\frac{8 m - 3}{5} = 1$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$5, 1$

Step 2.2

The LCM of one and any expression is the expression.

$5$

Step 3

Multiply each term in $\frac{8 m - 3}{5} = 1$ by $5$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{8 m - 3}{5} = 1$ by $5$ .

$\frac{8 m - 3}{5} \cdot 5 = 1 \cdot 5$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{8 m - 3}{5} \cdot 5 = 1 \cdot 5$

Step 3.2.1.2

Rewrite the expression.

$8 m - 3 = 1 \cdot 5$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $5$ by $1$ .

$8 m - 3 = 5$

Step 4

Solve the equation.

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Step 4.1

Move all terms not containing $m$ to the right side of the equation.

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Step 4.1.1

Add $3$ to both sides of the equation.

$8 m = 5 + 3$

Step 4.1.2

Add $5$ and $3$ .

$8 m = 8$

Step 4.2

Divide each term in $8 m = 8$ by $8$ and simplify.

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Step 4.2.1

Divide each term in $8 m = 8$ by $8$ .

$\frac{8 m}{8} = \frac{8}{8}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $8$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{8 m}{8} = \frac{8}{8}$

Step 4.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{8}{8}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $8$ by $8$ .

$m = 1$