Add. Simplify, if possible.
-$$\frac { m - 4 } { m ^ { 2 } - 6 m + 5 } + \frac { 4 m - 3 } { m ^ { 2 } - 9 m + 20 }$$
A) $\frac { 5 m ^ { 2 } - 15 m + 19 } { ( m - 5 ) ( m - 1 ) ( m - 4 ) }$
B) $5 \mathrm {~m} - 7$
C) $\frac { 5 m ^ { 2 } - 15 m + 19 } { ( m + 5 ) ( m + 1 ) ( m + 4 ) }$
D) $\frac { 5 m - 7 } { 2 m ^ { 2 } - 15 m + 25 }$

Question

Quizplus · Accepted Answer

To add the fractions, first factor the denominators: $m^2 - 6m + 5 = (m-5)(m-1)$ and $m^2 - 9m + 20 = (m-5)(m-4)$. The common denominator is $(m-5)(m-1)(m-4)$. After finding a common denominator and combining the numerators, the simplified form matches choice A.

Add Simplify, If Possible m−4m2−6m+5+4m−3m2−9m+20\frac { m - 4 } { m ^ { 2 } - 6 m + 5 } + \frac { 4 m - 3 } { m ^ { 2 } - 9 m + 20 }m2−6m+5m−4​+m2−9m+204m−3​

Add Simplify, If Possible $\frac { m - 4 } { m ^ { 2 } - 6 m + 5 } + \frac { 4 m - 3 } { m ^ { 2 } - 9 m + 20 }$