Basic Math Examples

\frac{m \cdot 40}{m - 40} \cdot (f o r m) = 101

$\frac{m \cdot 40}{m - 40} \cdot (f o r m) = 101$

Step 1

Factor each term.

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Step 1.1

Multiply

\frac{m \cdot 40}{m - 40}

$\frac{m \cdot 40}{m - 40}$ by

f o r m

$f o r m$ .

\frac{m \cdot 40}{m - 40} (f o r m) = 101

$\frac{m \cdot 40}{m - 40} (f o r m) = 101$

Step 1.2

Combine

f

$f$ and

\frac{m \cdot 40}{m - 40}

$\frac{m \cdot 40}{m - 40}$ .

\frac{f (m \cdot 40)}{m - 40} (o r m) = 101

$\frac{f (m \cdot 40)}{m - 40} (o r m) = 101$

Step 1.3

Combine

o

$o$ and

\frac{f (m \cdot 40)}{m - 40}

$\frac{f (m \cdot 40)}{m - 40}$ .

\frac{o (f (m \cdot 40))}{m - 40} (r m) = 101

$\frac{o (f (m \cdot 40))}{m - 40} (r m) = 101$

Step 1.4

Combine

r

$r$ and

\frac{o (f (m \cdot 40))}{m - 40}

$\frac{o (f (m \cdot 40))}{m - 40}$ .

\frac{r (o (f (m \cdot 40)))}{m - 40} m = 101

$\frac{r (o (f (m \cdot 40)))}{m - 40} m = 101$

Step 1.5

Combine

\frac{r (o (f (m \cdot 40)))}{m - 40}

$\frac{r (o (f (m \cdot 40)))}{m - 40}$ and

m

$m$ .

\frac{r (o (f (m \cdot 40))) m}{m - 40} = 101

$\frac{r (o (f (m \cdot 40))) m}{m - 40} = 101$

Step 1.6

Raise

m

$m$ to the power of

1

$1$ .

\frac{r (o (f \cdot (40))) (m^{1} m)}{m - 40} = 101

$\frac{r (o (f \cdot (40))) (m^{1} m)}{m - 40} = 101$

Step 1.7

Raise

$m$ to the power of

$1$ .

$\frac{r (o (f \cdot (40))) (m^{1} m^{1})}{m - 40} = 101$

Step 1.8

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{r (o (f \cdot (40))) m^{1 + 1}}{m - 40} = 101$

Step 1.9

Add

$1$ and

$1$ .

$\frac{r (o (f \cdot (40))) m^{2}}{m - 40} = 101$

Step 1.10

Remove parentheses.

$\frac{r (o f \cdot 40) m^{2}}{m - 40} = 101$

Step 1.11

Remove parentheses.

$\frac{r (o f) \cdot 40 m^{2}}{m - 40} = 101$

Step 1.12

Remove parentheses.

$\frac{r o f \cdot 40 m^{2}}{m - 40} = 101$

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.

$m - 40, 1$

Step 2.2

Remove parentheses.

$m - 40, 1$

Step 2.3

The LCM of one and any expression is the expression.

$m - 40$

Step 3

Multiply each term in

$\frac{r o f \cdot 40 m^{2}}{m - 40} = 101$ by

$m - 40$ to eliminate the fractions.

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Step 3.1

Multiply each term in

$\frac{r o f \cdot 40 m^{2}}{m - 40} = 101$ by

$m - 40$ .

$\frac{r o f \cdot 40 m^{2}}{m - 40} (m - 40) = 101 (m - 40)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$m - 40$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{r o f \cdot 40 m^{2}}{m - 40} (m - 40) = 101 (m - 40)$

Step 3.2.1.2

Rewrite the expression.

$r o f \cdot 40 m^{2} = 101 (m - 40)$

Step 3.2.2

Move

$40$ to the left of

$r o f$ .

$40 r o f m^{2} = 101 (m - 40)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$40 r o f m^{2} = 101 m + 101 \cdot - 40$

Step 3.3.2

Multiply

$101$ by

$- 40$ .

$40 r o f m^{2} = 101 m - 4040$

Step 4

Solve the equation.

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Step 4.1

Subtract

$101 m$ from both sides of the equation.

$40 r o f m^{2} - 101 m = - 4040$

Step 4.2

Add

$4040$ to both sides of the equation.

$40 r o f m^{2} - 101 m + 4040 = 0$

Step 4.3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4.4

Substitute the values

$a = 40 r o f$ ,

$b = - 101$ , and

$c = 4040$ into the quadratic formula and solve for

$m$ .

$\frac{101 \pm \sqrt{{(- 101)}^{2} - 4 \cdot (40 r o f \cdot 4040)}}{2 (40 r o f)}$

Step 4.5

Simplify.

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Step 4.5.1

Simplify the numerator.

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Step 4.5.1.1

Raise

$- 101$ to the power of

$2$ .

$m = \frac{101 \pm \sqrt{10201 - 4 \cdot (40 r o f) \cdot 4040}}{2 \cdot (40 r o f)}$

Step 4.5.1.2

Multiply

$- 4$ by

$40$ .

$m = \frac{101 \pm \sqrt{10201 - 160 r o f \cdot 4040}}{2 \cdot (40 r o f)}$

Step 4.5.1.3

Multiply

$4040$ by

$- 160$ .

$m = \frac{101 \pm \sqrt{10201 - 646400 r o f}}{2 \cdot (40 r o f)}$

Step 4.5.1.4

Factor

$101$ out of

$10201 - 646400 r o f$ .

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Step 4.5.1.4.1

Factor

$101$ out of

$10201$ .

$m = \frac{101 \pm \sqrt{101 (101) - 646400 r o f}}{2 \cdot (40 r o f)}$

Step 4.5.1.4.2

Factor

$101$ out of

$- 646400 r o f$ .

$m = \frac{101 \pm \sqrt{101 (101) + 101 (- 6400 r o f)}}{2 \cdot (40 r o f)}$

Step 4.5.1.4.3

Factor

$101$ out of

$101 (101) + 101 (- 6400 r o f)$ .

$m = \frac{101 \pm \sqrt{101 (101 - 6400 r o f)}}{2 \cdot (40 r o f)}$

Step 4.5.2

Multiply

$2$ by

$40$ .

$m = \frac{101 \pm \sqrt{101 (101 - 6400 r o f)}}{80 r o f}$

Step 4.6

The final answer is the combination of both solutions.

$m = \frac{101 + \sqrt{101 (101 - 6400 r o f)}}{80 r o f}$

$m = \frac{101 - \sqrt{101 (101 - 6400 r o f)}}{80 r o f}$

$m = \frac{101 + \sqrt{101 (101 - 6400 r o f)}}{80 r o f}$

$m = \frac{101 - \sqrt{101 (101 - 6400 r o f)}}{80 r o f}$