Multiply and simplify. 4 − r 5 ⋅ 5 r − 4 \frac { 4 - r } { 5 } \cdot \frac { 5 } { r - 4 } 5 4 − r ⋅ r − 4 5 A) − 1 , r ≠ 4 - 1 , r
eq 4 − 1 , r  = 4 B) − 4 5 , r ≠ 5 - \frac { 4 } { 5 } , r
eq 5 − 5 4 , r  = 5 C) 1 , r ≠ 4 1 , r
eq 4 1 , r  = 4 D) 5 4 , r ≠ − 5 \frac { 5 } { 4 } , r
eq - 5 4 5 , r  = − 5 E) 1 5 , r ≠ 0 \frac { 1 } { 5 } , r
eq 0 5 1 , r  = 0

Question

Multiply and simplify.   4 − r 5 ⋅ 5 r − 4 \frac { 4 - r } { 5 } \cdot \frac { 5 } { r - 4 } 5 4 − r ​ ⋅ r − 4 5 ​ A)    − 1 , r ≠ 4 - 1 , r 
eq 4 − 1 , r  = 4 B)    − 4 5 , r ≠ 5 - \frac { 4 } { 5 } , r 
eq 5 − 5 4 ​ , r  = 5 C)    1 , r ≠ 4 1 , r 
eq 4 1 , r  = 4 D)    5 4 , r ≠ − 5 \frac { 5 } { 4 } , r 
eq - 5 4 5 ​ , r  = − 5 E)    1 5 , r ≠ 0 \frac { 1 } { 5 } , r 
eq 0 5 1 ​ , r  = 0

Zybrea Knight · Accepted Answer

Final Answer : A, Explanation :   The expression simplifies to   − 1 -1 − 1   because the factors in the numerator and denominator are inverses of each other, with a sign change due to the order of   r r r   and   4 4 4  . The condition   r ≠ 4 r 
eq 4 r  = 4   ensures the denominator is not zero.

Multiply and simplify. $4−r5⋅5r−4\frac { 4 - r } { 5 } \cdot \frac { 5 } { r - 4 }$

A) $\neq 4$
B) $\frac { 4 } { 5 } , r \neq 5$
C) $\neq 4$
D) $54,r≠−5\frac { 5 } { 4 } , r \neq - 5$
E) $15,r≠0\frac { 1 } { 5 } , r \neq 0$

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