Combine and simplify. 13 2 + 4 x − 4 x + 1 \frac { 13 } { 2 } + \frac { 4 } { x } - \frac { 4 } { x + 1 } 2 13 + x 4 − x + 1 4 A) 13 x + 21 2 x ( x + 1 ) \frac { 13 x + 21 } { 2 x ( x + 1 ) } 2 x ( x + 1 ) 13 x + 21 B) 13 x 2 + 17 x + 4 2 x ( x + 1 ) \frac { 13 x ^ { 2 } + 17 x + 4 } { 2 x ( x + 1 ) } 2 x ( x + 1 ) 13 x 2 + 17 x + 4 C) 21 2 x ( x + 1 ) \frac { 21 } { 2 x ( x + 1 ) } 2 x ( x + 1 ) 21 D) 13 x 2 + 13 x + 8 2 x ( x + 1 ) \frac { 13 x ^ { 2 } + 13 x + 8 } { 2 x ( x + 1 ) } 2 x ( x + 1 ) 13 x 2 + 13 x + 8 E) 13 x + 17 2 x ( x + 1 ) \frac { 13 x + 17 } { 2 x ( x + 1 ) } 2 x ( x + 1 ) 13 x + 17

Question

Combine and simplify.   13 2 + 4 x − 4 x + 1 \frac { 13 } { 2 } + \frac { 4 } { x } - \frac { 4 } { x + 1 } 2 13 ​ + x 4 ​ − x + 1 4 ​ A)    13 x + 21 2 x ( x + 1 )  \frac { 13 x + 21 } { 2 x ( x + 1 )  } 2 x ( x + 1 )  13 x + 21 ​ B)    13 x 2 + 17 x + 4 2 x ( x + 1 )  \frac { 13 x ^ { 2 } + 17 x + 4 } { 2 x ( x + 1 )  } 2 x ( x + 1 )  13 x 2 + 17 x + 4 ​ C)    21 2 x ( x + 1 )  \frac { 21 } { 2 x ( x + 1 )  } 2 x ( x + 1 )  21 ​ D)    13 x 2 + 13 x + 8 2 x ( x + 1 )  \frac { 13 x ^ { 2 } + 13 x + 8 } { 2 x ( x + 1 )  } 2 x ( x + 1 )  13 x 2 + 13 x + 8 ​ E)    13 x + 17 2 x ( x + 1 )  \frac { 13 x + 17 } { 2 x ( x + 1 )  } 2 x ( x + 1 )  13 x + 17 ​

Alyssa Sanchez · Accepted Answer

Final Answer : D, Explanation :  To combine the three fractions, we need to find a common denominator. The common denominator is $(2x)(x+1)$. We can then rewrite the fractions with this denominator: $\frac{13(x+1)}{2(x+1)}+\frac{4(2x)}{2x(x+1)}-\frac{4(2)}{2(x+1)x}$. Simplifying each fraction, we get $\frac{13}{2}+\frac{8}{x+1}-\frac{4}{x}$.Taking a common denominator again, we get $\frac{13(x+1)}{2(x+1)}+\frac{8(2x)}{2x(x+1)}-\frac{4(2(x+1))}{2(x+1)x}$, which simplifies to $\frac{13x^2+13x+8}{2x(x+1)}$. Therefore, the answer is D.

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