Answer:
1. D
2.B
3.B
4.B
5. B
6.D
Step-by-step explanation:
QUESTION 1
We want to simplify [tex]\frac{\frac{2a+1}{10a-5}}{\frac{10a}{4a^2-1}}[/tex].
Let us change the middle bar to a normal division sign to obtain,
[tex]\frac{2a+1}{10a-5}\div\frac{10a}{4a^2-1}[/tex].
We now multiply, the first fraction by the reciprocal of the second fraction to get,
[tex]\frac{2a+1}{10a-5}\times \frac{4a^2-1}{10a}[/tex].
We now factor to obtain,
[tex]\frac{2a+1}{5(2a-1)}\times \frac{(2a-1)(2a+1)}{10a}[/tex].
We cancel out common factors to get,
[tex]\frac{2a+1}{5(1)}\times \frac{(1)(2a+1)}{10a}[/tex].
We now multiply out to get,
[tex]\frac{(2a+1)^2}{50a}[/tex].
Ans:D
QUESTION 2
The given expression is [tex]\frac{\frac{x}{x+4} }{x}[/tex]
We change the middle bar to a normal division sign to get,
[tex]\frac{x}{x+4}\div x[/tex]
We now multiply by the reciprocal of the second fraction to obtain,
[tex]\frac{x}{x+4}\times \frac{1}{x}[/tex]
Ans:B
QUESTION 3
We want to simplify the quotient,
[tex]\frac{\frac{n+3}{2n-6}}{\frac{n+3}{3n-9}}[/tex].
We change the middle to a normal division sign to obtain,
[tex]\frac{n+3}{2n-6}\div\frac{n+3}{3n-9}[/tex].
We now multiply the first fraction by the reciprocal of the second fraction to get,
[tex]\frac{n+3}{2n-6}\times \frac{3n-9}{n+3}[/tex].
We factor to get,
[tex]\frac{n+3}{2(n-3)}\times \frac{3(n-3)}{n+3}[/tex].
We cancel out common factors to obtain,
[tex]\frac{1}{2(1)}\times \frac{3(1)}{1}[/tex].
We simplify to get,
[tex]\frac{3}{2}[/tex].
Ans:B
QUESTION 4
We want to find the product [tex]\frac{a-3}{15a} \times\frac{5}{a-3}[/tex].
This multiplication is very simple to do. We just have to cancel out common factors to get,
[tex]\frac{1}{3a} \times\frac{1}{1}[/tex].
We now multiply out to get,
[tex]\frac{1}{3a}[/tex]
Ans:B
QUESTION 5.
We want to find the product [tex]\frac{2a-7}{a} \times \frac{3a^2}{2a^2-11a+14}[/tex].
We factor the denominator of the second fraction to obtain,
[tex]\frac{2a-7}{a} \times \frac{3a^2}{(2a-7)(a-2)}[/tex].
We now cancel out common factors to obtain,
[tex]\frac{1}{1} \times \frac{3a}{(1)(a-2)}[/tex].
We multiply out to get,
[tex]\frac{3a}{a-2}[/tex].
Ans:B
QUESTION 6
We want to find the quotient [tex]\frac{\frac{a-3}{7}}{\frac{3-a}{21} }[/tex].
We need to change the middle bar to a normal division sign to get,
[tex]\frac{a-3}{7}\div \frac{3-a}{21}[/tex]
We multiply by the reciprocal of the second function to get,
[tex]\frac{a-3}{7} \times \frac{21}{3-a}[/tex]
We factor the negative 1 from the denominator of the second fraction to get,
[tex]\frac{a-3}{7} \times \frac{21}{-1(a-3)}[/tex]
We now cancel common factors to get,
[tex]\frac{1}{1} \times \frac{3}{-1(1)}[/tex]
This simplifies to,
[tex]-3[/tex].
Ans: D
Two questions repeated
