Simplify
5x+50/x+5*1/x+10
Answers
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