Polynomials and fractions

9000079208

Level: 
B
Assuming \(x\neq 0\) and \(y\neq 0\), simplify the following expression. \[ \left (\frac{x^{-2}y^{2}} {x^{0}y^{-8}}\right )^{-2} : \frac{x^{2}} {x^{-4}y^{7}} \]
\(\frac{1} {x^{2}y^{13}} \)
\(\frac{y^{13}} {x^{2}} \)
\(\frac{y^{15}} {x^{6}} \)
\(\frac{x^{4}} {y^{27}} \)

9000083607

Level: 
B
Assuming \(x\neq 0\), \(x\neq \pm 1\), \(y\neq 0\), simplify the expression. \[ \left [\left ( \frac{x} {x + 1}\right )^{2} : \left (\frac{x - 1} {y} \right )^{2}\right ] : \frac{2xy} {x^{2} - 1} \]
\(\frac{xy} {2\left (x^{2}-1\right )}\)
\(4\)
\(\frac{x^{2}-1} {4} \)
\(\frac{x-1} {4} \)

9000088807

Level: 
B
Suppose we are given the following equality of two fractions with nonzero denominators. From the given expressions, choose the one that by substituting to the starred position makes the equality true. \[ \frac{3 - 2x} {x - 2} = \frac{3(4x^{2} - 12x + 9)} {*} \]
\((3x - 6)(3 - 2x)\)
\((x - 2)(2x - 3)\)
\((x - 2)(9 - 4x)\)
\((3x - 6)(2x - 3)\)