Polynomials and fractions

9000088803

Level:

Evaluate the following expression at

x = \frac{1}{2}

1 - \frac{x - 2}{2 x + 1}

\frac{7}{4}

\frac{1}{4}

\frac{5}{4}

\frac{3}{4}

9000088804

Level:

Simplify the following expression.

\frac{2 s - 8 r s}{16 r^{2} - 1}

- \frac{2 s}{4 r + 1}

\frac{2 s}{4 r + 1}

\frac{2 s}{4 r - 1}

\frac{2 s}{1 - 4 r}

9000088805

Level:

Simplify the following expression.

\frac{a^{4} - 1}{1 - a^{2}}

- a^{2} - 1

a^{2} + 1

a^{2} - 1

1 - a^{2}

9000088809

Level:

Simplify the following expression.

(\frac{1}{m - n} - \frac{1}{m + n}) \cdot (\frac{m^{2} + 2 m n + n^{2}}{2 n})

\frac{m + n}{m - n}

0

\frac{m (m + n)}{n (m - n)}

2

9000088810

Level:

Simplify the following expression.

(x - \frac{1}{x}) \cdot (1 - \frac{x}{x + 1})

\frac{x - 1}{x}

\frac{x - 1}{x + 1}

\frac{1 - x}{x + 1}

\frac{1 - x}{x}

9000101601

Level:

Expand

(1 + x) (x^{2} + x - 1) (1 - x)

- x^{4} - x^{3} + 2 x^{2} + x - 1

x^{4} - x^{3} + 2 x^{2} + x + 1

- x^{4} + x^{3} - 1

x^{4} + x^{3} - 2 x^{2} + x - 1

9000101602

Level:

Simplify the polynomial

(x - 1) (x + 1) (x^{2} + 1) - {(x^{2} - 1)}^{2}

into one of the following forms.

2 (x^{2} - 1)

0

2 (x^{2} - 1) (x + 1)

x^{2} - 1

9000101603

Level:

Simplify the polynomial

(x + 1) (x - 1)^{2} - (x - 1) (x + 1)^{2}

into one of the following forms.

- 2 (x - 1) (x + 1)

2 (x - 1) (x + 1)

0

2

9000101604

Level:

Expand the polynomial

{(2 x^{2} + 4 x)}^{2} - {(4 x - 2 x^{2})}^{2}

32 x^{3}

0

32 x^{3} - 8 x

32 x^{3} - 32 x^{2} + 8 x

9000146203

Level:

Expand the following expression.

{(x^{5} - \sqrt{2} y)}^{2}

x^{10} - 2 \sqrt{2} x^{5} y + 2 y^{2}

x^{10} - \sqrt{2} x^{5} y + 2 y^{2}

x^{10} - 2 \sqrt{2} x^{5} y - 2 y^{2}

x^{10} - \sqrt{2} x^{5} y - 2 y^{2}

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Polynomials and fractions

9000088803

9000088804

9000088805

9000088809

9000088810

9000101601

9000101602

9000101603

9000101604

9000146203

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