Answer:
1. The correct answer option is B.
2. The correct answer option is C.
4. The correct answer option is D.
Step-by-step explanation:
1. [tex]\frac{3}{x^2+14x+48}[/tex] ÷ [tex]\frac{3}{10x+60}[/tex]
Changing division to multiplication by taking the reciprocal of the latter fraction:
[tex]\frac{3}{x^2+14x+48} \times \frac{10x+60}{3}[/tex]
[tex]\frac{3}{(x+6)(x+8)} \times \frac{10(x+6)}{3}[/tex]
Cancelling the like terms to get:
[tex]\frac{10}{(x+8)}[/tex]
The correct answer option is B. [tex]\frac{10}{(x+8)}[/tex]
2. [tex]\frac{4x^2+36}{4x} \times \frac{1}{5x}[/tex]
Factorizing the terms and then cancelling the like terms to get:
[tex]\frac{4(x^2+9)}{4x} \times \frac{1}{5x}[/tex]
[tex]\frac{x^2+9}{5x^2}[/tex]
The correct answer option is C. [tex]\frac{x^2+9}{5x^2}[/tex].
4. [tex]\frac{\frac{4t^2-16}{8} }{\frac{t-2}{6} }[/tex]
Changing division to multiplication by taking the reciprocal of the latter fraction:
[tex]\frac{4t^2-16}{8} \times \frac{6}{t-2}[/tex]
[tex]\frac{4(t-2)(t+2)}{8} \times \frac{6}{t-2}[/tex]
Cancelling the like terms to get:
[tex]3(t+2)[/tex]
The correct answer option is D. [tex]3(t+2)[/tex].
