Polynomials and fractions

2010006614

Level:

Assuming \( y\in \mathbb{R}\setminus \{-2;1;2\}\), simplify the expression: \[ \left( \frac{y+2}{y-1} - \frac{y+5}{y+2}\right)\cdot \left(y+\frac{y}{y-2}\right) \]

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

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

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

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

2010006613

Level:

Assuming \( x\in \mathbb{R}\setminus \{-1;2;1\}\), simplify the expression: \[\left( \frac{x-1}{x-2} - \frac{x}{x-1}\right)\cdot \left(x-\frac{3x}{x+1}\right) \]

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

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

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

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

2010006612

Level:

Assuming \( x \in \mathbb{R}\setminus \{\pm 2\}\), simplify the expression: \[ \left[\frac{2}{x+2} -\frac{2}{(x+2)^2}+\frac{2}{x^2-4}\right]\cdot \frac{x^2+ 4x+4}{3}\]

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

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

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

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

2010006611

Level:

Assuming \( x \in \mathbb{R}\setminus \{\pm 3\}\), simplify the expression: \[\left[\frac{3}{(x-3)^2} +\frac{1}{x+3}+\frac{6}{x^2-9}\right]\cdot \frac{x^2-6x+9}{2}\]

\( \frac{x}2 \)

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

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

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

2010006610

Level:

Assuming \( a \in \mathbb{R}\setminus \{-4; 0; 4\}\), simplify the expression: \[ \frac{3}{2a^2-8a} +2- \frac{1+2a^2}{a^2-16}\]

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

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

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

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

2010006609

Level:

Assuming \( x \in \mathbb{R}\setminus \{-3; 0; 3\}\), simplify the expression: \[ \frac{5}{2x^2+6x} - \frac{4-3x^2}{x^2-9}-3\]

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

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

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

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

2010006608

Level:

Assuming \(x \neq \pm y\), simplify the expression: \[ \frac{x-2y}{x+y} - \frac{2x-y}{y-x} - \frac{2x^2}{x^2-y^2}\]

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

\( \frac{xy}{x^2-y^2}\)

\( \frac{xy}{y^2-x^2}\)

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

2010006607

Level:

Assuming \(a \neq \pm x\), simplify the expression: \[ \frac{a}{a-x} - \frac{3a}{a+x} + \frac{2ax}{x^2-a^2}\]

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

\( \frac{4a}{a+x}\)

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

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

2010006606

Level:

Assuming \(a\neq 0\), \(b\neq 0\), \(c\neq 0\), simplify the expression: \[ \frac{5a-c}{6ac} - \frac{2a-3b}{12ab}-\frac{3}{4a}-\frac{2c-3b}{3bc}\]

\( \frac{11ab-5ac-4bc}{6abc} \)

\( \frac{11ab-5ac-5bc}{6abc} \)

\( \frac{-ab-5ac-7bc}{6abc} \)

\( 0\)

2010006605

Level:

Assuming \(a\neq 0\), \(b\neq 0\), \(c\neq 0\), simplify the expression: \[ \frac{2a-c}{4c} - \frac{3a^2-2ab}{6ac}-\frac{2a}{3c}-\frac{5a-b}{2b}\]

\( \frac{4b^2-8ab-30ac+3bc}{12bc} \)

\( \frac{-4b^2-8ab-30ac+3bc}{12bc} \)

\( \frac{4b^2-8ab-30ac-9bc}{12bc} \)

\( 0\)

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Polynomials and fractions

2010006614

2010006613

2010006612

2010006611

2010006610

2010006609

2010006608

2010006607

2010006606

2010006605

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