Simplifying Rational ExpressionsSimplify the following rational expression: 5 / ( x + 3 ) − 7 x / ( x − 1 )I came across this question in my homework and because it is a fraction, I decided that I needed to establish a common denominator of: x − 3But how do I convert x - 1 into x-3 ?

Question

Simplifying Rational ExpressionsSimplify the following rational expression:   5      /    (  x  +  3  )  −  7  x      /    (  x  −  1  )I came across this question in my homework and because it is a fraction, I decided that I needed to establish a common denominator of:  x  −  3But how do I convert x - 1 into x-3 ?

szabadotttt3dg · Accepted Answer

Notice, we can simplify the given expression as follows      5          x      +      3        −            7      x              x      −      1        =      5          x      +      3        −            7      x      −      7      +      7              x      −      1        =      5          x      +      3        −            7      (      x      −      1      )      +      7              x      −      1        =      5          x      +      3        −            7      (      x      −      1      )              x      −      1        −      7          x      −      1        =      5          x      +      3        −  7  −      7          x      −      1        =  −  7  +      5          x      +      3        −      7          x      −      1      orUsing partial fraction      5          x      +      3        −            7      x              x      −      1        =            5      (      x      −      1      )      −      7      x      (      x      +      3      )              (      x      +      3      )      (      x      −      1      )        =            5      x      −      5      −      7              x        2            −      21      x              (      x      +      3      )      (      x      −      1      )        =            −      7              x        2            −      16      x      −      5              (      x      +      3      )      (      x      −      1      )        =            −      (      7              x        2            +      16      x      +      5      )              (      x      +      3      )      (      x      −      1      )        =  −  7  −            2      x      +      26              (      x      +      3      )      (      x      −      1      )        =  −  7  −            2      (      x      +      13      )              (      x      −      1      )      (      x      −      3      )      Making partial fractions of             x      +      13              (      x      −      1      )      (      x      −      3      )        =      A          x      −      1        +      B          x      +      3          ⟹    A  =      7    2    ,     B  =  −      5    2  , we get            5              x        +        3              −                  7        x                    x        −        1              =      −    7    −          7              x        −        1              +          5              x        +        3

Simplifying Rational Expressions Simplify the following rational expression: 5 <mrow class="

Answered question

Answer & Explanation

New Questions in Pre-Algebra