Math, asked by siddiquiz5865, 1 year ago

Simplify
    
5x+50/x+5*1/x+10

Answers

Answered by janvi754
2
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Answered by Anudesigner
1

Final result :

 5 • (x2 + 2x + 11)

 ——————————————————

         x          

Step by step solution :

Step  1  :

           1

Simplify   —

           x

Equation at the end of step  1  :

         50          1      

 ((5x +  ——) +  (5 • —)) +  10

         x           x      

Step  2  :

           50

Simplify   ——

           x  

Equation at the end of step  2  :

         50     5      

 ((5x +  ——) +  —) +  10

         x      x      

Step  3  :

Rewriting the whole as an Equivalent Fraction :

  Adding a fraction to a whole

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

          5x     5x • x

    5x =  ——  =  ——————

          1        x    

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:

5x • x + 50     5x2 + 50

———————————  =  ————————

     x             x    

Equation at the end of step  3  :

  (5x2 + 50)    5      

 (—————————— +  —) +  10

      x         x      

Step  4  :

Step  5  :

Pulling out like terms :

     Pull out like factors :

  5x2 + 50  =   5 • (x2 + 10)  

5 • (x2+10) + 5     5x2 + 55

———————————————  =  ————————

       x               x    

Equation at the end of step  5  :

 (5x2 + 55)    

 —————————— +  10

     x          

Step  6  :

Rewriting the whole as an Equivalent Fraction :

6.1   Adding a whole to a fraction

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

         10     10 • x

   10 =  ——  =  ——————

         1        x    

Step  7  :

Pulling out like terms :

7.1     Pull out like factors :

  5x2 + 55  =   5 • (x2 + 11)  

5 • (x2+11) + 10 • x     5x2 + 10x + 55

————————————————————  =  ——————————————

         x                     x        

Step  8  :

Pulling out like terms :

8.1     Pull out like factors :

  5x2 + 10x + 55  =   5 • (x2 + 2x + 11)  

Trying to factor by splitting the middle term

   Factoring  x2 + 2x + 11  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +2x  its coefficient is  2 .

The last term, "the constant", is  +11  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 11 = 11  

Step-2 : Find two factors of  11  whose sum equals the coefficient of the middle term, which is   2 .

     -11    +    -1    =    -12  

     -1    +    -11    =    -12  

     1    +    11    =    12  

     11    +    1    =    12  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 5 • (x2 + 2x + 11)

 ——————————————————

         x

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