2010006607
Level:
B
Assuming \(a \neq \pm x\), simplify the expression: \[ \frac{a}{a-x} - \frac{3a}{a+x} + \frac{2ax}{x^2-a^2}\]
\( \frac{-2a}{a+x}\)
\( \frac{4a}{a+x}\)
\( \frac{2a(3x-a)}{x^2-a^2}\)
\( \frac{2a(3x-a)}{a^2-x^2}\)
Polynomials and fractions
2010006608
Level:
B
Assuming \(x \neq \pm y\), simplify the expression: \[ \frac{x-2y}{x+y} - \frac{2x-y}{y-x} - \frac{2x^2}{x^2-y^2}\]
\( \frac{x-y}{x+y}\)
\( \frac{xy}{x^2-y^2}\)
\( \frac{xy}{y^2-x^2}\)
\( \frac{y-x}{x+y}\)
2010006609
Level:
B
Assuming \( x \in \mathbb{R}\setminus \{-3; 0; 3\}\), simplify the expression:
\[ \frac{5}{2x^2+6x} - \frac{4-3x^2}{x^2-9}-3\]
\( \frac{3(17x-5)}{2x(x^2-9)} \)
\( \frac{-3(19x-5)}{2x(x^2-9)} \)
\( \frac{3(5-19x)}{2x(x^2-9)} \)
\( \frac{3(5-17x)}{2x(x^2-9)} \)
2010006610
Level:
B
Assuming \( a \in \mathbb{R}\setminus \{-4; 0; 4\}\), simplify the expression:
\[ \frac{3}{2a^2-8a} +2- \frac{1+2a^2}{a^2-16}\]
\( \frac{3(4-21a)}{2a(a^2-16)} \)
\( \frac{3(21a-4)}{2a(a^2-16)} \)
\( \frac{3(21a-4)}{a(a^2-16)} \)
\( \frac{3(4-21a)}{a(a^2-16)} \)
2010006611
Level:
B
Assuming \( x \in \mathbb{R}\setminus \{\pm 3\}\), simplify the expression:
\[\left[\frac{3}{(x-3)^2} +\frac{1}{x+3}+\frac{6}{x^2-9}\right]\cdot \frac{x^2-6x+9}{2}\]
\( \frac{x}2 \)
\( \frac{x^2}2 \)
\( \frac{x(x-3)}{2(x+3)} \)
\( \frac{x(x+3)}{2(x-3)} \)
2010006612
Level:
B
Assuming \( x \in \mathbb{R}\setminus \{\pm 2\}\), simplify the expression:
\[ \left[\frac{2}{x+2} -\frac{2}{(x+2)^2}+\frac{2}{x^2-4}\right]\cdot \frac{x^2+
4x+4}{3}\]
\( \frac{2x^2}{3(x-2)} \)
\( \frac{2x^2}{3(x+2)} \)
\( \frac{x^2}{3(x+2)} \)
\( \frac{x^2}{3(x-2)} \)
2010006613
Level:
B
Assuming \( x\in \mathbb{R}\setminus \{-1;2;1\}\), simplify the expression:
\[\left( \frac{x-1}{x-2} - \frac{x}{x-1}\right)\cdot \left(x-\frac{3x}{x+1}\right) \]
\( \frac{x}{x^2-1}\)
\( \frac{x}{1-x^2}\)
\( \frac{x(1-4x)}{x^2-1}\)
\( \frac{x(4x-1)}{x^2-1}\)
2010006614
Level:
B
Assuming \( y\in \mathbb{R}\setminus \{-2;1;2\}\), simplify the expression:
\[ \left( \frac{y+2}{y-1} - \frac{y+5}{y+2}\right)\cdot \left(y+\frac{y}{y-2}\right) \]
\( \frac{9y}{y^2-4}\)
\( \frac{9y}{4-y^2}\)
\( \frac{y(8y-1)}{y^2-4}\)
\( \frac{y(1-8y)}{y^2-4}\)
2010007301
Level:
B
Factoring the polynomial \( -8x^3+12x^2+8x \) you get:
\( -4x(2x+1)(x-2) \)
\( 4x(-2x+1)(x-2) \)
\( -4x(2x-1)(x+2) \)
\( 4x(-2x+1)(x+2) \)
2010008807
Level:
B
Factor the expression: \[9(3t - 2z)^2 - 16(t - 2z)^2\]
\((5t + 2z)(13t - 14z)\)
\((5t + 2z)(3t - 4z)\)
\((5t - 14z)(13t - 14z)\)
\((5t - 14z)(3t - 4z)\)