3. Reduce the fraction −20t 5u 2v 3

48t 7u 4v
.
A. −5t 2v 2
12u 2 C. −5v 2
12t 2u 2
B. 5t 2v 2
12u 2 D. 5v 2
12t 2u 2
4. Reduce the fraction
w 2 + 5w + 6
w 2 − w − 12
.
A. w − 2
w − 4
C. w + 2
w + 4
B. w + 2
w − 4
D. w − 2
w + 4
5. Find the illegal values of b in the fraction
2b 2 + 3b − 10
b 2 − 2b − 8
.
A. b = −5 and 2 C. b = −2 and 4
B. b = −2 and −4 D. b = −5, −2, 2 and 4
6. Multiply 3xyz 2
6y 4 by 2y
xz 4.
A. 1
y 2z 2 C. x 2
3y 2z 2
B. x 2
y 2z 2
D. 1
3y 2z 2
88

3. To reduce the fraction -20t^5u^2v^3/48t^7u^4v, we need to simplify the numerator and denominator separately, and then divide the simplified numerator by the simplified denominator.

For the numerator:
-20t^5u^2v^3 can be simplified as -5t^2v^2 (by dividing each exponent by the corresponding exponent in the denominator).

For the denominator:
48t^7u^4v can be simplified as 12t^2u^2 (by dividing each exponent by the corresponding exponent in the numerator).

Now, we divide the simplified numerator (-5t^2v^2) by the simplified denominator (12t^2u^2):
(-5t^2v^2)/(12t^2u^2) can be further simplified as -5v^2/(12u^2).

Therefore, the reduced fraction is -5v^2/(12u^2).
The correct answer is C. -5v^2/(12u^2).

4. To reduce the fraction (w^2 + 5w + 6)/(w^2 - w - 12), we need to factorize the numerator and denominator, and then cancel out any common factors.

Factorizing the numerator:
(w^2 + 5w + 6) can be factored as (w + 3)(w + 2).

Factorizing the denominator:
(w^2 - w - 12) can be factored as (w - 4)(w + 3).

Now, we can cancel out the common factor of (w + 3) in the numerator and denominator:
[(w + 3)(w + 2)]/[(w - 4)(w + 3)] simplifies to (w + 2)/(w - 4).

Therefore, the reduced fraction is (w + 2)/(w - 4).
The correct answer is B. (w + 2)/(w - 4).

5. To find the illegal values of b in the fraction (2b^2 + 3b - 10)/(b^2 - 2b - 8), we need to find the values of b that make the denominator equal to 0 (since division by 0 is undefined).

To find the values of b that satisfy b^2 - 2b - 8 = 0, we can factorize the quadratic equation:
(b - 4)(b + 2) = 0

Setting each factor equal to 0:
b - 4 = 0 -> b = 4
b + 2 = 0 -> b = -2

Therefore, the values b = 4 and b = -2 make the denominator equal to 0, which are illegal values for b.

The correct answer is B. b = -2 and -4.

6. To multiply 3xyz^2/(6y^4) by 2y/xz^4, we need to multiply the numerators together and the denominators together.

Multiplying the numerators:
3xyz^2 * 2y = 6xyz^3y

Multiplying the denominators:
(6y^4) * (xz^4) = 6xy^4z^4

Putting the multiplied parts together, we get:
(6xyz^3y)/(6xy^4z^4)

Simplifying the numerator and denominator by canceling common factors:
6xyz^3y / (6xy^4z^4) = 1 / (yz)

Therefore, the result of the multiplication is 1/(yz).
The correct answer is A. 1/(yz).