Solution - Reducing fractions to their lowest terms
Other Ways to Solve
Reducing fractions to their lowest termsStep by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step 1 :
6
Simplify —
7
Equation at the end of step 1 :
6
((((7•(x2))+11x)-(—•x2))-10x)+3
7
Step 2 :
Equation at the end of step 2 :
6x2 ((((7•(x2))+11x)-———)-10x)+3 7Step 3 :
Equation at the end of step 3 :
6x2
(((7x2 + 11x) - ———) - 10x) + 3
7
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 7 as the denominator :
7x2 + 11x (7x2 + 11x) • 7
7x2 + 11x = ————————— = ———————————————
1 7
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
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
7x2 + 11x = x • (7x + 11)
Adding fractions that have a common denominator :
5.2 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:
x • (7x+11) • 7 - (6x2) 43x2 + 77x
——————————————————————— = ——————————
7 7
Equation at the end of step 5 :
(43x2 + 77x)
(———————————— - 10x) + 3
7
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 7 as the denominator :
10x 10x • 7
10x = ——— = ———————
1 7
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
43x2 + 77x = x • (43x + 77)
Adding fractions that have a common denominator :
7.2 Adding up the two equivalent fractions
x • (43x+77) - (10x • 7) 43x2 + 7x
———————————————————————— = —————————
7 7
Equation at the end of step 7 :
(43x2 + 7x)
——————————— + 3
7
Step 8 :
Rewriting the whole as an Equivalent Fraction :
8.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 7 as the denominator :
3 3 • 7
3 = — = —————
1 7
Step 9 :
Pulling out like terms :
9.1 Pull out like factors :
43x2 + 7x = x • (43x + 7)
Adding fractions that have a common denominator :
9.2 Adding up the two equivalent fractions
x • (43x+7) + 3 • 7 43x2 + 7x + 21
——————————————————— = ——————————————
7 7
Trying to factor by splitting the middle term
9.3 Factoring 43x2 + 7x + 21
The first term is, 43x2 its coefficient is 43 .
The middle term is, +7x its coefficient is 7 .
The last term, "the constant", is +21
Step-1 : Multiply the coefficient of the first term by the constant 43 • 21 = 903
Step-2 : Find two factors of 903 whose sum equals the coefficient of the middle term, which is 7 .
| -903 | + | -1 | = | -904 | ||
| -301 | + | -3 | = | -304 | ||
| -129 | + | -7 | = | -136 | ||
| -43 | + | -21 | = | -64 | ||
| -21 | + | -43 | = | -64 | ||
| -7 | + | -129 | = | -136 | ||
| -3 | + | -301 | = | -304 | ||
| -1 | + | -903 | = | -904 | ||
| 1 | + | 903 | = | 904 | ||
| 3 | + | 301 | = | 304 | ||
| 7 | + | 129 | = | 136 | ||
| 21 | + | 43 | = | 64 | ||
| 43 | + | 21 | = | 64 | ||
| 129 | + | 7 | = | 136 | ||
| 301 | + | 3 | = | 304 | ||
| 903 | + | 1 | = | 904 |
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
43x2 + 7x + 21
——————————————
7
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