(3m+1/a)x2 +(11+m/b)x +9/c=0
Answers
Step 1 :
9
Simplify —
c
Equation at the end of step 1 :
1 m 9
(((3m+—)•(x2))+((11+—)•x))+— = 0
a b c
Step 2 :
m
Simplify —
b
Equation at the end of step 2 :
1 m 9
(((3m+—)•(x2))+((11+—)•x))+— = 0
a b c
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Adding a fraction to a whole
Rewrite the whole as a fraction using b as the denominator :
11 11 • b
11 = —— = ——————
1 b
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 :
3.2 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:
11 • b + m m + 11b
—————————— = ———————
b b
Equation at the end of step 3 :
1 (m+11b) 9
(((3m+—)•(x2))+(———————•x))+— = 0
a b c
Step 4 :
Equation at the end of step 4 :
1 x•(m+11b) 9
(((3m+—)•(x2))+—————————)+— = 0
a b c
Step 5 :
1
Simplify —
a
Equation at the end of step 5 :
1 x • (m + 11b) 9
(((3m + —) • x2) + —————————————) + — = 0
a b c
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Adding a fraction to a whole
Rewrite the whole as a fraction using a as the denominator :
3m 3m • a
3m = —— = ——————
1 a
Adding fractions that have a common denominator :
6.2 Adding up the two equivalent fractions
3m • a + 1 3ma + 1
—————————— = ———————
a a
Equation at the end of step 6 :
(3ma + 1) x • (m + 11b) 9
((————————— • x2) + —————————————) + — = 0
a b c
Step 7 :
Equation at the end of step 7 :
x2 • (3ma + 1) x • (m + 11b) 9
(—————————————— + —————————————) + — = 0
a b c
Step 8 :
Calculating the Least Common Multiple :
8.1 Find the Least Common Multiple
The left denominator is : a
The right denominator is : b
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
a 1 0 1
b 0 1 1
Least Common Multiple:
ab
Calculating Multipliers :
8.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = b
Right_M = L.C.M / R_Deno = a
Making Equivalent Fractions :
8.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. x2 • (3ma+1) • b
—————————————————— = ————————————————
L.C.M ab
R. Mult. • R. Num. x • (m+11b) • a
—————————————————— = ———————————————
L.C.M ab
Adding fractions that have a common denominator :
8.4 Adding up the two equivalent fractions
x2 • (3ma+1) • b + x • (m+11b) • a 3max2b + max + 11axb + x2b
—————————————————————————————————— = ——————————————————————————
ab ab
Equation at the end of step 8 :
(3max2b + max + 11axb + x2b) 9
———————————————————————————— + — = 0
ab c
Step 9 :
Step 10 :
Pulling out like terms :
10.1 Pull out like factors :
3max2b + max + 11axb + x2b =
x • (3maxb + ma + 11ab + xb)
Calculating the Least Common Multiple :
10.2 Find the Least Common Multiple