Finite Math Examples

x = u (\frac{u \cdot (1 - u)}{s} - 1)

$x = u (\frac{u \cdot (1 - u)}{s} - 1)$

Step 1

Simplify

u (\frac{u \cdot (1 - u)}{s} - 1)

$u (\frac{u \cdot (1 - u)}{s} - 1)$ .

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Step 1.1

To write

- 1

$- 1$ as a fraction with a common denominator, multiply by

\frac{s}{s}

$\frac{s}{s}$ .

x = u (\frac{u (1 - u)}{s} - 1 \cdot \frac{s}{s})

$x = u (\frac{u (1 - u)}{s} - 1 \cdot \frac{s}{s})$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine

- 1

$- 1$ and

\frac{s}{s}

$\frac{s}{s}$ .

x = u (\frac{u (1 - u)}{s} + \frac{- s}{s})

$x = u (\frac{u (1 - u)}{s} + \frac{- s}{s})$

Step 1.2.2

Combine the numerators over the common denominator.

x = u (\frac{u (1 - u) - s}{s})

$x = u (\frac{u (1 - u) - s}{s})$

x = u (\frac{u (1 - u) - s}{s})

$x = u (\frac{u (1 - u) - s}{s})$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Apply the distributive property.

x = u (\frac{u \cdot 1 + u (- u) - s}{s})

$x = u (\frac{u \cdot 1 + u (- u) - s}{s})$

Step 1.3.2

Multiply

u

$u$ by

1

$1$ .

x = u (\frac{u + u (- u) - s}{s})

$x = u (\frac{u + u (- u) - s}{s})$

Step 1.3.3

Rewrite using the commutative property of multiplication.

x = u (\frac{u - u \cdot u - s}{s})

$x = u (\frac{u - u \cdot u - s}{s})$

Step 1.3.4

Multiply

u

$u$ by

u

$u$ by adding the exponents.

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Step 1.3.4.1

Move

u

$u$ .

x = u (\frac{u - (u \cdot u) - s}{s})

$x = u (\frac{u - (u \cdot u) - s}{s})$

Step 1.3.4.2

Multiply

u

$u$ by

u

$u$ .

x = u (\frac{u - u^{2} - s}{s})

$x = u (\frac{u - u^{2} - s}{s})$

x = u (\frac{u - u^{2} - s}{s})

$x = u (\frac{u - u^{2} - s}{s})$

x = u (\frac{u - u^{2} - s}{s})

$x = u (\frac{u - u^{2} - s}{s})$

x = u (\frac{u - u^{2} - s}{s})

$x = u (\frac{u - u^{2} - s}{s})$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be

0

$0$ or

1

$1$ for each of its variables. In this case, the degree of variable

x

$x$ is

1

$1$ , the degree of variable

u

$u$ is

3

$3$ , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

Not Linear