Polynomials and fractions

2010006607

Level:

Assuming

a \neq \pm x

, simplify the expression:

\frac{a}{a - x} - \frac{3 a}{a + x} + \frac{2 a x}{x^{2} - a^{2}}

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

\frac{4 a}{a + x}

\frac{2 a (3 x - a)}{x^{2} - a^{2}}

\frac{2 a (3 x - a)}{a^{2} - x^{2}}

2010006608

Level:

Assuming

x \neq \pm y

, simplify the expression:

\frac{x - 2 y}{x + y} - \frac{2 x - y}{y - x} - \frac{2 x^{2}}{x^{2} - y^{2}}

\frac{x - y}{x + y}

\frac{x y}{x^{2} - y^{2}}

\frac{x y}{y^{2} - x^{2}}

\frac{y - x}{x + y}

2010006609

Level:

Assuming

x \in R ∖ {- 3; 0; 3}

, simplify the expression:

\frac{5}{2 x^{2} + 6 x} - \frac{4 - 3 x^{2}}{x^{2} - 9} - 3

\frac{3 (17 x - 5)}{2 x (x^{2} - 9)}

\frac{- 3 (19 x - 5)}{2 x (x^{2} - 9)}

\frac{3 (5 - 19 x)}{2 x (x^{2} - 9)}

\frac{3 (5 - 17 x)}{2 x (x^{2} - 9)}

2010006610

Level:

Assuming

a \in R ∖ {- 4; 0; 4}

, simplify the expression:

\frac{3}{2 a^{2} - 8 a} + 2 - \frac{1 + 2 a^{2}}{a^{2} - 16}

\frac{3 (4 - 21 a)}{2 a (a^{2} - 16)}

\frac{3 (21 a - 4)}{2 a (a^{2} - 16)}

\frac{3 (21 a - 4)}{a (a^{2} - 16)}

\frac{3 (4 - 21 a)}{a (a^{2} - 16)}

2010006611

Level:

Assuming

x \in R ∖ {\pm 3}

, simplify the expression:

[\frac{3}{(x - 3)^{2}} + \frac{1}{x + 3} + \frac{6}{x^{2} - 9}] \cdot \frac{x^{2} - 6 x + 9}{2}

\frac{x}{2}

\frac{x^{2}}{2}

\frac{x (x - 3)}{2 (x + 3)}

\frac{x (x + 3)}{2 (x - 3)}

2010006612

Level:

Assuming

x \in R ∖ {\pm 2}

, simplify the expression:

[\frac{2}{x + 2} - \frac{2}{(x + 2)^{2}} + \frac{2}{x^{2} - 4}] \cdot \frac{x^{2} + 4 x + 4}{3}

\frac{2 x^{2}}{3 (x - 2)}

\frac{2 x^{2}}{3 (x + 2)}

\frac{x^{2}}{3 (x + 2)}

\frac{x^{2}}{3 (x - 2)}

2010006613

Level:

Assuming

x \in R ∖ {- 1; 2; 1}

, simplify the expression:

(\frac{x - 1}{x - 2} - \frac{x}{x - 1}) \cdot (x - \frac{3 x}{x + 1})

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

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

\frac{x (1 - 4 x)}{x^{2} - 1}

\frac{x (4 x - 1)}{x^{2} - 1}

2010006614

Level:

Assuming

y \in R ∖ {- 2; 1; 2}

, simplify the expression:

(\frac{y + 2}{y - 1} - \frac{y + 5}{y + 2}) \cdot (y + \frac{y}{y - 2})

\frac{9 y}{y^{2} - 4}

\frac{9 y}{4 - y^{2}}

\frac{y (8 y - 1)}{y^{2} - 4}

\frac{y (1 - 8 y)}{y^{2} - 4}

2010007301

Level:

Factoring the polynomial

- 8 x^{3} + 12 x^{2} + 8 x

you get:

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

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

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

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

2010008807

Level:

Factor the expression:

9 (3 t - 2 z)^{2} - 16 (t - 2 z)^{2}

(5 t + 2 z) (13 t - 14 z)

(5 t + 2 z) (3 t - 4 z)

(5 t - 14 z) (13 t - 14 z)

(5 t - 14 z) (3 t - 4 z)

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Polynomials and fractions

2010006607

2010006608

2010006609

2010006610

2010006611

2010006612

2010006613

2010006614

2010007301

2010008807

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