Are these complex fractions equivalent ?

Question

Are the complex fractions the quantity x-squared minus x minus 20 over 4 all over the quantity x minus 5 over 10 and the quantity x-squared minus x minus 20 over x minus 5 all over the quantity 4 over 10 equivalent? Simplify each, and then explain why or why not.

Answer 1

*The software doesn't show underlines. So you can't see the fraction bars I put in. 

There should be fraction bars in between numbers and variables that are stacked.

 

 

It sounds like the question is: are these two rational expressions equal?

 

   x²- x - 20                 x² - x - 20     

       4                             (x-5)

___________        =   ____________

 

    (x-5)                            4__

     10                              10

 

 

Step 1: Remember the rule about fractions: when you divide you multiply by the reciprocal. (The sign changes to multiplication and the second fraction is flipped.) So each side becomes this:

 

Left Side:

x²- x - 20     Times       10

     4                          (x-5)    

 

 

Right Side:

x² - x - 20      Times   10

   x-5                          4

 

 

 

Step 2: Factor your polynomials and remember to cross reduce. Then multiply. The (x-5) can be taken out and the 4 and the 10 reduced by 2.

 

Left side:

(x-5) (x + 4)   Times        10
    4                               (x-5)

 

 

Right side:

(x - 5) (x + 4)   Times       10
      (x-5)                           4

 

 

 

 

Step 3: Compare. Yes they are equal!

 

Left side:

5(x + 4)

    2

 

 

Right side:

5(x+ 4)

    2