Finite Math Examples

$y = t u^{5} u^{6} \cdot (5 u^{6}) \cdot (7 u i j) + 2$

Step 1

Rewrite the equation as $t u^{5} u^{6} \cdot (5 u^{6}) \cdot (7 u i j) + 2 = y$ .

$t u^{5} u^{6} \cdot (5 u^{6}) \cdot (7 u i j) + 2 = y$

Step 2

Simplify each term.

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Step 2.1

Multiply $u^{5}$ by $u^{6}$ by adding the exponents.

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Step 2.1.1

Move $u^{6}$ .

$t (u^{6} u^{5}) \cdot (5 u^{6}) \cdot (7 u i j) + 2 = y$

Step 2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t u^{6 + 5} \cdot (5 u^{6}) \cdot (7 u i j) + 2 = y$

Step 2.1.3

Add $6$ and $5$ .

$t u^{11} \cdot (5 u^{6}) \cdot (7 u i j) + 2 = y$

Step 2.2

Multiply $u^{11}$ by $u^{6}$ by adding the exponents.

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Step 2.2.1

Move $u^{6}$ .

$t (u^{6} u^{11}) \cdot 5 \cdot (7 u i j) + 2 = y$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t u^{6 + 11} \cdot 5 \cdot (7 u i j) + 2 = y$

Step 2.2.3

Add $6$ and $11$ .

$t u^{17} \cdot 5 \cdot (7 u i j) + 2 = y$

Step 2.3

Multiply $u^{17}$ by $u$ by adding the exponents.

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Step 2.3.1

Move $u$ .

$t (u \cdot u^{17}) \cdot 5 \cdot (7 i j) + 2 = y$

Step 2.3.2

Multiply $u$ by $u^{17}$ .

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Step 2.3.2.1

Raise $u$ to the power of $1$ .

$t (u^{1} u^{17}) \cdot 5 \cdot (7 i j) + 2 = y$

Step 2.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t u^{1 + 17} \cdot 5 \cdot (7 i j) + 2 = y$

Step 2.3.3

Add $1$ and $17$ .

$t u^{18} \cdot 5 \cdot (7 i j) + 2 = y$

Step 2.4

Move $5$ to the left of $t u^{18}$ .

$5 \cdot (t u^{18}) \cdot (7 i j) + 2 = y$

Step 2.5

Multiply $7$ by $5$ .

$35 t u^{18} i j + 2 = y$

Step 3

Subtract $2$ from both sides of the equation.

$35 t u^{18} i j = y - 2$

Step 4

Divide each term in $35 t u^{18} i j = y - 2$ by $35 t u^{18} i$ and simplify.

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Step 4.1

Divide each term in $35 t u^{18} i j = y - 2$ by $35 t u^{18} i$ .

$\frac{35 t u^{18} i j}{35 t u^{18} i} = \frac{y}{35 t u^{18} i} + \frac{- 2}{35 t u^{18} i}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $35$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{35 t u^{18} i j}{35 t u^{18} i} = \frac{y}{35 t u^{18} i} + \frac{- 2}{35 t u^{18} i}$

Step 4.2.1.2

Rewrite the expression.

$\frac{t u^{18} i j}{t u^{18} i} = \frac{y}{35 t u^{18} i} + \frac{- 2}{35 t u^{18} i}$

Step 4.2.2

Cancel the common factor of $t$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{t u^{18} i j}{t u^{18} i} = \frac{y}{35 t u^{18} i} + \frac{- 2}{35 t u^{18} i}$

Step 4.2.2.2

Rewrite the expression.

$\frac{u^{18} i j}{u^{18} i} = \frac{y}{35 t u^{18} i} + \frac{- 2}{35 t u^{18} i}$

Step 4.2.3

Cancel the common factor of $u^{18}$ .

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Step 4.2.3.1

Cancel the common factor.

$\frac{u^{18} i j}{u^{18} i} = \frac{y}{35 t u^{18} i} + \frac{- 2}{35 t u^{18} i}$

Step 4.2.3.2

Rewrite the expression.

$\frac{i j}{i} = \frac{y}{35 t u^{18} i} + \frac{- 2}{35 t u^{18} i}$

Step 4.2.4

Cancel the common factor of $i$ .

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Step 4.2.4.1

Cancel the common factor.

$\frac{i j}{i} = \frac{y}{35 t u^{18} i} + \frac{- 2}{35 t u^{18} i}$

Step 4.2.4.2

Divide $j$ by $1$ .

$j = \frac{y}{35 t u^{18} i} + \frac{- 2}{35 t u^{18} i}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$j = \frac{y}{35 t u^{18} i} - \frac{2}{35 t u^{18} i}$