Question

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

Answer 1

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

Explanation:

12) Lowest Common Denominator of

`(p+3)/(p^2+7p+10) \,\, and \,\, (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

`(p+3)/((p+5)(p+2)) \,\, and \,\, (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

`(40x)/(64y) \,\,by\,\, (5x)/(8y)`

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

`(40x)/(64y)/(5x)/(8y)`

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

`(40x)/(64y)*(8y)/(5x)\\\\Solving\\(40x*8y)/(64y*5x)\\\\(320xy)/(320xy) \\\\1`

So, Option A is correct.

14. Simplify:

`(x+2)/(x^2-6x-16) / (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,

`(x+2)/((x-8)(x+2)) * (9x)/(1)\\(9x)/(x-8)`

So, Option C is correct.

15. Simplify

`(4)/((1)/(4)-(5)/(2))`

Solving denominator,

Taking LCM of 4 and 2 and subtracting we get

`(4)/((1-(5*2))/(4))\\(4)/((1-10)/(4))\\(4)/((-9)/(4))\\(4*4)/(-9)\\(16)/(-9) \,\,or\,\,\\(-16)/(9)`

Option D is correct.

16. Simplify:

`(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,

`(7(x+6))/((x+7)(x+6))\\\\Cancelling\,\, x+6 \,\, from\,\, numerator \,\, and\,\, \\\\(7)/((x+7))`

Option A is correct.