Question

1. What are the excluded values?

y+5
________
y^2+4y-32

A) y = -5 and 4
B) y = 5 and 32
C) y = 4 and -8
D) none of the above

2. What are the excluded values?

-7z
___
4z+1

A) z=-4
B) z= -1/4
C) z= -1/7
D) none of the above

3. What are the excluded values?

m+5
______
mn+3m

A) m = -5, n = -3
B) m = 0, n = -3
C) m = -3, n = 0

4. Reduce to lowest terms.

6a^2b^3
______
8ab^4

A) 3b/4a
B) 3a/4b
C) 3/4ab

5. Reduce to lowest terms.

3-k
___
k-3

A) -1
B) 1
C) -1/3

Answer 1

Answers are as follows
1 C
2 B
3 B
4 B
5 A

Answer 2

Answer:

correct option is (C)

Step-by-step explanation:

Q 1.)

$\frac{y+5}{y^2+4y-32}$

To find excluded values, we equate denominator of above expression to zero:

$y^2+4y-32=0$

solve above expression by middle term splitting,

$y^2+8y-4y-32 =0$

factor out GCF,

$y(y+8)-4(y+8)=0$

factor out the common terms,

$(y+8)(y-4) =0$

$(y+8)=0\,or\,(y-4)=0$

$y=-8\,or\,y=4$

Hence, the correct option is (C)

Q 2.)

$\frac{-7z}{4z+1}$

To find excluded values, we equate denominator of above expression to zero:

$4z+1 =0$

subtract 1 from both the sides,

$4z+1-1 =-1$

$4z=-1$

divide both the side by 4,

$z=\frac{-1}{4}$

Hence, the correct option is (B).

Q 3.)

$\frac{m+5}{mn+3m}$

To find excluded values, we equate denominator of above expression to zero:

$mn+3m=0$

Take common factor out 'm',

$m(n+3)=0$

$m=0,n+3=0$

$m=0,n=-3$

Hence, the correct option is (B)

Q 4.)

$\frac{6a^2b^3}{8ab^4}$

To reduce tom lowest term, cancel out the common denominators term with numerators;

$\frac{6a^2b^3}{8ab^4}$

Using the low of exponent \frac{a^n}{a^m}=a^n-m,

$\frac{6a^{2-1}b^{3-4}}{8}$

$\frac{6a^{1}b^{-1}}{8}$

so,

$\frac{6a}{8b}$

$\frac{3a}{4b}$

Hence, the correct option is (B)

Q 5.)

$\frac{3-k}{k-3}$

To reduce tom lowest term, cancel out the common denominators term with numerators;

$(-1) \frac{k-3}{k-3}$

$-1$

Hence, the correct option is (A)