Simplify \(\frac{1}{p}\) - \(\frac{1}{q}\) \(\div\) \(\frac{p}{q}\) - \(\frac{q}{p}\)
\(\frac{1}{p - q}\)
\(\frac{-1}{p + q}\)
\(\frac{1}{pq}\)
\(\frac{1}{pq(p - q)}\)
Correct answer is B
\(\frac{1}{p}\) - \(\frac{1}{q}\) \(\div\) \(\frac{p}{q}\) - \(\frac{q}{p}\) = \(\frac{q - p}{pq}\) ÷ \(\frac{p^2 - q^2}{pq}\)
\(\frac{q - p}{pq}\) x \(\frac{pq}{p^2q^2}\) = \(\frac{q - p}{p^2 - q^2}\)
\(\frac{-(p - q)}{(p + q)(p - q)}\)
= \(\frac{-1}{p + q}\)
Divide the expression x3 + 7x2 - x - 7 by -1 + x2
-x3 + 7x2 - x - 7
-x3 = 7x + 7
x - 7
x + 7
Correct answer is D
No explanation has been provided for this answer.
If the function f is defined by f(x + 2) = 2x\(^2\) + 7x - 5, find f(-1)
-10
-8
4
10
Correct answer is B
f(x + 2) = f(-1)
f(-1) is gotten when x = -3.
\(2x^{2} + 7x - 5\) at x = -3.
f(-1) = \(2(-3)^{2} + 7(-3) - 5\)
= \(18 - 21 - 5 = -8\)
Solve the following equation (3x - 2)(5x - 4) = (3x - 2)2
\(\frac{-2}{3}\), 1
1
\(\frac{2}{3}\), 1
\(\frac{2}{3}\), \(\frac{4}{5}\)
Correct answer is C
(3x - 2)(5x - 4) = (3x - 2)2 = 5x2 - 22x + 6
= 9x2 = 12x + 4
6x2 - 10x + 4 = 0
6x2 - 6x - 4x + 4 = 0
6x(x - 1) -4(x - 1) = (6x - 4)(x -1) = 0
x = 1 or \(\frac{2}{3}\)
Solve the following simultaneous equation for x. x2 + y - 5 = 0, y - 7x + 3 = 0
-2, 4
2, 4
-1,8
1, -8
Correct answer is D
x2 + y - 5 = 0.....(i)
y - 7x + 3 = 0.........(ii)
y = 7x - 3, substituting the value of y in equation (i)
x2 + (7x - 3) - 5 = 0
x2 + 7x + 3 = 0
(x + 8)(x - 1) = 0
x = -8 or 1