Answer:
correct option is (C)
Step-by-step explanation:
Q 1.)
[tex]\frac{y+5}{y^2+4y-32}[/tex]
To find excluded values, we equate denominator of above expression to zero:
[tex]y^2+4y-32=0[/tex]
solve above expression by middle term splitting,
[tex]y^2+8y-4y-32 =0[/tex]
factor out GCF,
[tex]y(y+8)-4(y+8)=0[/tex]
factor out the common terms,
[tex](y+8)(y-4) =0[/tex]
[tex](y+8)=0\,or\,(y-4)=0[/tex]
[tex]y=-8\,or\,y=4[/tex]
Hence, the correct option is (C)
Q 2.)
[tex]\frac{-7z}{4z+1}[/tex]
To find excluded values, we equate denominator of above expression to zero:
[tex]4z+1 =0[/tex]
subtract 1 from both the sides,
[tex]4z+1-1 =-1[/tex]
[tex]4z=-1[/tex]
divide both the side by 4,
[tex]z=\frac{-1}{4}[/tex]
Hence, the correct option is (B).
Q 3.)
[tex]\frac{m+5}{mn+3m}[/tex]
To find excluded values, we equate denominator of above expression to zero:
[tex]mn+3m=0[/tex]
Take common factor out 'm',
[tex]m(n+3)=0[/tex]
[tex]m=0,n+3=0[/tex]
[tex]m=0,n=-3[/tex]
Hence, the correct option is (B)
Q 4.)
[tex]\frac{6a^2b^3}{8ab^4}[/tex]
To reduce tom lowest term, cancel out the common denominators term with numerators;
[tex]\frac{6a^2b^3}{8ab^4}[/tex]
Using the low of exponent \frac{a^n}{a^m}=a^n-m,
[tex]\frac{6a^{2-1}b^{3-4}}{8}[/tex]
[tex]\frac{6a^{1}b^{-1}}{8}[/tex]
so,
[tex]\frac{6a}{8b}[/tex]
[tex]\frac{3a}{4b}[/tex]
Hence, the correct option is (B)
Q 5.)
[tex]\frac{3-k}{k-3}[/tex]
To reduce tom lowest term, cancel out the common denominators term with numerators;
[tex](-1) \frac{k-3}{k-3}[/tex]
[tex]-1[/tex]
Hence, the correct option is (A)
