QUESTION 5
The given equation is:
[tex] \frac{5}{a + 3} = \frac{3}{a - 2} [/tex]
Cross multiply;
[tex]5(a - 2) = 3(a + 3)[/tex]
Expand:
5a-10=3a+9
Group similar terms:
5a-3a=9+10
2a=19
Divide both sides by 2
[tex]a = \frac{19}{2} [/tex]
[tex]a = 9\frac{1}{2} [/tex]
The correct answer is C.
QUESTION 7
The given equation is:
[tex] \frac{3}{y - 2}= 8[/tex]
There is an invisible 1 in the denominator on the RHS.
[tex] \frac{3}{y - 2}= \frac{8}{1} [/tex]
Cross multiply:
[tex] 3\times 1 = 8(y - 2)[/tex]
Expand:
[tex]3= 8y - 16[/tex]
Group similar terms,
[tex]3 + 16 = 8y[/tex]
[tex]19 = 8y[/tex]
Divide both sides by 8.
[tex]y = \frac{19}{8} [/tex]
[tex]y = 2 \frac{3}{8} [/tex]
The correct answer is C.
QUESTION 8
The given fraction is:
[tex] \frac{ {w}^{2} + 5w + 6}{ {w}^{2} - w - 12 } [/tex]
Factor both the numerator and the denominator to obtain:
[tex] \frac{(w + 3)(w + 2)}{(w + 3)(w - 4)} [/tex]
Cancel the common factors;
[tex]\frac{w + 2}{w - 4} [/tex]
The correct answer is B.
QUESTION 9
The given expression is;
[tex] \frac{3m}{m - 6} \times \frac{5 {m}^{3} - 30 {m}^{2} }{5 {m}^{2} } [/tex]
Factor the numerator of the second fraction.
[tex]\frac{3m}{m - 6} \times \frac{5 {m}^{2}(m - 6)}{5 {m}^{2} }[/tex]
Cancel the common factors,
[tex] \frac{3m}{1} [/tex]
[tex] = 3m[/tex]
The correct answer is D.
QUESTION 10
The given expression is:
[tex] \frac{7x + 21}{ {x}^{2} + 5x + 6} \div \frac{x + 6}{x + 2} [/tex]
Multiply by the reciprocal of the second fraction.
[tex]\frac{7x + 21}{ {x}^{2} + 5x + 6} \times \frac{x + 2}{x + 6} [/tex]
Factor the first fraction to get:
[tex]\frac{7(x + 3)}{ (x + 2)(x + 3)} \times \frac{x + 2}{x + 6} [/tex]
Cancel the common factors:
[tex] \frac{7}{x + 6} [/tex]
The correct answer is A.
