Question

PLEASE HELP!!! NEED ANSWERS TO THESE QUESTIONS..

Answer 1

Answer:

12. Option A is correct

13. Option A is correct

14. Option C is correct

15. Option D is correct

16. Option A is correct

Step-by-step explanation:

12) Lowest Common Denominator of

$\frac{p+3}{p^2+7p+10} \,\, and \,\, \frac{p+5}{p^2+5p+6}$

We should find the factors of denominators and then find the LCM of the denominators.Finding LCD is same as finding LCM.

Factors of p^2+7p+10 = p^2 +2p +5p+10 = p(p+2)+5(p+2) = (p+5)(p+2)

Factors of p^2+5p+6 = p^2+2p+3p+6 = p(p+2)+3(p+2) = (p+3) (p+2)

Now, rewriting the above equation with factors and finding the LCM

$\frac{p+3}{(p+5)(p+2)} \,\, and \,\, \frac{p+5}{(p+3)(p+2)}$

LCM of (p+5)(p+2) and (p+3)(p+2) = (p+5)(p+3)(p+2)

The LCD is (p+5)(p+3)(p+2).

So, Option A is correct.

13. Divide

$\frac{40x}{64y} \,\,by\,\, \frac{5x}{8y}$

by stands for division. The equation can be written as:

$\frac{40x}{64y}\div\frac{5x}{8y}$

Division sign changed into multiplication, we take reciprocal of second term i.e,

$\frac{40x}{64y}*\frac{8y}{5x}\\\\Solving\\\frac{40x*8y}{64y*5x}\\\\\frac{320xy}{320xy} \\\\1$

So, Option A is correct.

14. Simplify:

$\frac{x+2}{x^2-6x-16} \div \frac{1}{9x}$

Factors of x^2-6x-16= x^2 -8x +2x -16 = x(x-8)+2(x-8) = (x-8)(x+2)

Putting factors in the above equation and changing division sign with multiplication we get,

$\frac{x+2}{(x-8)(x+2)} * \frac{9x}{1}\\\frac{9x}{x-8}$

So, Option C is correct.

15. Simplify

$\frac{4}{\frac{1}{4}-\frac{5}{2}}$

Solving denominator,

Taking LCM of 4 and 2 and subtracting we get

$\frac{4}{\frac{1-(5*2)}{4}}\\\frac{4}{\frac{1-10}{4}}\\\frac{4}{\frac{-9}{4}}\\\frac{4*4}{-9}\\\frac{16}{-9} \,\,or\,\,\\\frac{-16}{9}$

Option D is correct.

16. Simplify:

$\frac{7x+42}{x^2+13x+42}$

Making factors of x^2+13x+42= x^2 +6x+7x+42 = x(x+6)+7(x+6) = (x+7)(x+6)

Taking 7 common from numerator and putting factors in denominator we get,

$\frac{7(x+6)}{(x+7)(x+6)}\\\\Cancelling\,\, x+6 \,\, from\,\, numerator \,\, and\,\, \\\\\frac{7}{(x+7)}$

Option A is correct.