Perform the indicated operation. Simplify, if possible.
-$$\frac { b } { b ^ { 2 } - 25 } + \frac { 5 } { b + 5 } - \frac { 6 } { b }$$
A) $\frac { 25 ( b - 6 ) } { ( b + 5 ) ( b - 5 ) }$

B) $\frac { - 25 ( b - 6 ) } { b ( b + 5 ) ( b - 5 ) }$

C) $\frac { 25 ( b + 6 ) } { b ( b + 5 ) ( b - 5 ) }$

D) $\frac { 6 b ^ { 2 } - 25 b + 150 } { b ( b + 5 ) ( b - 5 ) }$

Question

Perform the indicated operation. Simplify, if possible.
-$$\frac { b } { b ^ { 2 } - 25 } + \frac { 5 } { b + 5 } - \frac { 6 } { b }$$
A) $\frac { 25 ( b - 6 ) } { ( b + 5 ) ( b - 5 ) }$

B) $\frac { - 25 ( b - 6 ) } { b ( b + 5 ) ( b - 5 ) }$

C) $\frac { 25 ( b + 6 ) } { b ( b + 5 ) ( b - 5 ) }$

D) $\frac { 6 b ^ { 2 } - 25 b + 150 } { b ( b + 5 ) ( b - 5 ) }$

Quizplus · Accepted Answer

To simplify the given expression, first, recognize that the denominators can be related through factoring and common denominators. The first term has a denominator that factors into $(b+5)(b-5)$, the second term already has a part of this factor $(b+5)$, and the third term's denominator is $b$. The least common denominator (LCD) for all three fractions is $b(b+5)(b-5)$. Rewriting each fraction with the LCD as the denominator:1. $\frac{b}{(b+5)(b-5)}$ becomes $\frac{b}{(b+5)(b-5)}\cdot\frac{b}{b} = \frac{b^2}{b(b+5)(b-5)}$2. $\frac{5}{b+5}$ becomes $\frac{5}{b+5}\cdot\frac{b(b-5)}{b(b-5)} = \frac{5b(b-5)}{b(b+5)(b-5)}$3. $\frac{6}{b}$ becomes $\frac{6}{b}\cdot\frac{(b+5)(b-5)}{(b+5)(b-5)} = \frac{6(b+5)(b-5)}{b(b+5)(b-5)}$Adding these fractions together:$\frac{b^2 + 5b(b-5) - 6(b^2-25)}{b(b+5)(b-5)}$Simplifying the numerator:$b^2 + 5b^2 - 25b - 6b^2 + 150$This simplifies to:$-25b + 150$So, the simplified expression is:$\frac{-25b + 150}{b(b+5)(b-5)}$However, this does not match any of the given options directly because of a simplification oversight. The correct approach involves combining the fractions correctly and simplifying the numerator accurately, considering the common denominator. The correct answer involves recognizing the algebraic manipulation and simplification process that leads to the expression in option B, which correctly represents the algebraic manipulation of the given fractions into a single fraction with the denominator $b(b+5)(b-5)$ and a numerator that simplifies to a form similar to the options provided. The mistake in the simplification process above indicates a misstep in combining and simplifying the terms correctly. The correct answer, B, reflects the proper algebraic process to reach the simplified form of the given expression, considering the negative sign that emerges from correctly combining and simplifying the terms in the numerator relative to the common denominator.

Perform the Indicated Operation bb2−25+5b+5−6b\frac { b } { b ^ { 2 } - 25 } + \frac { 5 } { b + 5 } - \frac { 6 } { b }b2−25b​+b+55​−b6​

Perform the Indicated Operation $\frac { b } { b ^ { 2 } - 25 } + \frac { 5 } { b + 5 } - \frac { 6 } { b }$