Question

I need answer for these questions please

Answer 1

QUESTION 5

The given equation is:

`(5)/(a + 3) = (3)/(a - 2)`

Cross multiply;

`5(a - 2) = 3(a + 3)`

Expand:

5a-10=3a+9

Group similar terms:

5a-3a=9+10

2a=19

Divide both sides by 2

`a = (19)/(2)`

`a = 9(1)/(2)`

The correct answer is C.

QUESTION 7

The given equation is:

`(3)/(y - 2)= 8`

There is an invisible 1 in the denominator on the RHS.

`(3)/(y - 2)= (8)/(1)`

Cross multiply:

`3* 1 = 8(y - 2)`

Expand:

`3= 8y - 16`

Group similar terms,

`3 + 16 = 8y`

`19 = 8y`

Divide both sides by 8.

`y = (19)/(8)`

`y = 2 (3)/(8)`

The correct answer is C.

QUESTION 8

The given fraction is:

`\frac{ {w}^(2) + 5w + 6}{ {w}^(2) - w - 12 }`

Factor both the numerator and the denominator to obtain:

`((w + 3)(w + 2))/((w + 3)(w - 4))`

Cancel the common factors;

`(w + 2)/(w - 4)`

The correct answer is B.

QUESTION 9

The given expression is;

`(3m)/(m - 6) * \frac{5 {m}^(3) - 30 {m}^(2) }{5 {m}^(2) }`

Factor the numerator of the second fraction.

`(3m)/(m - 6) * \frac{5 {m}^(2)(m - 6)}{5 {m}^(2) }`

Cancel the common factors,

`(3m)/(1)`

`= 3m`

The correct answer is D.

QUESTION 10

The given expression is:

`\frac{7x + 21}{ {x}^(2) + 5x + 6} / (x + 6)/(x + 2)`

Multiply by the reciprocal of the second fraction.

`\frac{7x + 21}{ {x}^(2) + 5x + 6} * (x + 2)/(x + 6)`

Factor the first fraction to get:

`(7(x + 3))/( (x + 2)(x + 3)) * (x + 2)/(x + 6)`

Cancel the common factors:

`(7)/(x + 6)`

The correct answer is A.