Solve rational Equation

Please Show Full Steps Please!

Answer:

x=1

Step-by-step

Step 1:

Simplify x/x2

Dividing exponential expressions :  

1.1    x1 divided by x2 = x(1 - 2) = x(-1) = 1/x1 = 1/

Equation at the end of step 1:

  2    1         1

 (((—+1)-—)-1)-((2•—)-1)  = 0

    x    x         x

STEP 2:Rewriting the whole as an Equivalent Fraction:

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  x  as the denominator :

        1     1 • x

   1 =  —  =  —————

        1       x  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2 - (x)     2 - x

——— = ———  

   x          x  

Equation at the end of step 2:

2    1     (2-x)

 (((—+1)-—)-1)-—————  = 0

    x    x       x  

STEP 3:

Simplify 1/x

Equation at the end of step 3:

2          1           (2 - x)

 (((— +  1) -  —) -  1) -  ———————  = 0

    x          x              x  

STEP4:

Simplify: 2/x

Equation at the end of step 4:

    2          1                 (2 - x)

 (((— +  1) -  —) -  1) -  ———————  = 0

    x          x                      x  

STEP 5:

Rewriting the whole as an Equivalent Fraction :

5.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  x  as the denominator :

        1         1 • x

   1 =  —  =  —————

        1            x  

Adding fractions that have a common denominator :

5.2       Adding up the two equivalent fractions

2 + x                x + 2

—————  =  —————

  x                       x  

Equation at the end of step 5:

(x + 2)    1                                (2 - x)

 ((——————— -  —) -  1) -  ———————  = 0

      x       x                                  x  

STEP 6:Adding fractions which have a common denominator :

Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(x+2) - (1)                            x + 1

———————————  =  —————

     x                                       x

Equation at the end of step 6:

  (x + 1)                           (2 - x)

 (——————— -  1) -  ———————  = 0

     x                               x

STEP 7:

Rewriting the whole as an Equivalent Fraction :

7.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  x  as the denominator :

        1     1 • x

   1 =  —  =  —————

        1       x  

Adding fractions that have a common denominator :

7.2       Adding up the two equivalent fractions

(x+1) - (x)                           1

———————————  =  —

     x                                   x

Equation at the end of step 7:

 1       (2 - x)

 — -  ———————  = 0

 x         x

STEP 8:

Adding fractions which have a common denominator :

8.1       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

1 - ((2-x))                              x - 1

———————————  =  —————

     x                                     x    

Equation at the end of step 8:

 x - 1

 —————  = 0

   x  

STEP 9:

When a fraction equals zero :

9.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 x-1

 ——— • x = 0 • x

  x

Now, on the left hand side, the  x  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  x-1  = 0

.2      Solve  :    x-1 = 0

Add  1  to both sides of the equation :

                     x = 1

One solution was found :

x = 1

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