2010008805
Level:
A
Simplify: \[- ab(a + b) - a[3b^2 - a(2a + 5b) - b(3b - 4a)]\]
\(a(2a^2 - b^2)\)
\(a(2a^2 - 7b^2)\)
\(a(2a^2 + 8ab - 7b^2)\)
\(a(2a^2 + 8ab - b^2)\)
Polynomials and fractions
2010008806
Level:
A
Simplify: \[a^2(3a - b) -[b^2(a + 3b) -b(3b^2 + ab - a^2) - 3a^3]\]
\(2a^2(3a - b)\)
\(-2b^2(a + 3b)\)
\(2(3a^3 - 3b^3 - ab^2)\)
\(6(a^3 - b^3)\)
9000079201
Level:
A
Evaluate
\[
\frac{-x^{2}}
{x - y} -\frac{y - x}
{x + y}
\]
at \(x = -1\),
\(y = 2\).
\(-\frac{8}
{3}\)
\(-\frac{10}
{3} \)
\(-\frac{2}
{3}\)
\(-\frac{4}
{3}\)
9000079205
Level:
A
Assuming \(x\neq 0\)
and \(x\neq 2\),
simplify the following expression.
\[
\frac{x^{3} - x^{2}}
{x - 2} \cdot \frac{2 - x}
{x^{2}}
\]
\(1 - x\)
\(x - 1\)
\(x + 1\)
\(x^{2} - 1\)
9000079206
Level:
A
Assuming \(x\neq 0\),
\(y\neq 0\),
\(x\neq y\),
simplify the following expression.
\[ {
\frac{1}
{x^{2}} - \frac{1}
{y^{2}}
\over -\frac{1}
{y} + \frac{1}
{x}}
\]
\(\frac{x+y}
{xy} \)
\(-\frac{x+y}
{xy} \)
\(\frac{1}
{y} -\frac{1}
{x}\)
\(\frac{1}
{x} -\frac{1}
{y}\)
9000079210
Level:
A
Consider the expression
\[
V (x) = \frac{x}
{x - 1} - \frac{1}
{1 - x}.
\]
Find the correct ordering of the values
\(V (-2)\),
\(V (0)\) and
\(V (2)\).
\(V (0) < V (-2) < V (2)\)
\(V (-2) < V (0) < V (2)\)
\(V (0) < V (2) < V (-2)\)
\(V (2) < V (0) < V (-2)\)
9000083602
Level:
A
Evaluate the following expression at \(x = \frac{1}
{2}\).
\[
\frac{x^{2} - 2}
{1 -\frac{1}
{x}}
\]
\(\frac{7}
{4}\)
\(-\frac{7}
{4}\)
\(\frac{7}
{2}\)
\(-\frac{7}
{2}\)
9000083603
Level:
A
Evaluate the following expression at \(x = \frac{1}
{2}\)
and \(y = -\frac{1}
{4}\).
\[
\frac{x -\frac{y}
{x}}
{1 + \frac{x}
{y}}
\]
\(- 1\)
\(3\)
\(4\)
\(1\)
9000083604
Level:
A
Assuming \(x\neq - 1\),
\(x\neq \pm y\),
simplify the expression.
\[
\frac{x^{2} + 2xy + y^{2}}
{2x^{2} + 4x + 2} \cdot \frac{(x + 1)(y - x)}
{y^{2} - x^{2}}
\]
\(\frac{x+y}
{2x+2}\)
\(\frac{x+y}
{2} \)
\(x + y\)
\(\frac{1}
{2}\)
9000083605
Level:
A
Find the common denominator of the fractions.
\[
\text{$ \frac{3x}
{x^{2}+4x+4}$ and $ \frac{x+5}
{x^{2}-4}$}
\]
\((x + 2)^{2}(x - 2),\; x\neq \pm 2\)
\((x + 2)(x - 4),\; x\neq \pm 2\)
\((x + 2)^{2}(x - 4),\; x\neq \pm 2\)
\((x + 2)(x - 4),\; x\neq \pm 2\)