Question

Write as a single fraction:
(6x+4y/9x) - (6x-7y/3x)+2

Answer 1

Step by step solution :
Step 1 :

7xy
Simplify 6x - ———
3

Rewriting the whole as an Equivalent Fraction :

1.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 3 as the denominator :

6x 6x • 3
6x = —— = ——————
1 3

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 :

1.2 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:

6x • 3 - (7xy) 18x - 7xy
—————————————— = —————————
3 3

Equation at the end of step 1 :

y (18x-7xy)
((6x+((4•—)•x))-—————————)+2
9 3

Step 2 :

4xy
Simplify 6x + ———
9

Rewriting the whole as an Equivalent Fraction :

2.1 Adding a fraction to a whole

Rewrite the whole as a fraction using 9 as the denominator :

6x 6x • 9
6x = —— = ——————
1 9

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

6x • 9 + 4xy 4xy + 54x
———————————— = —————————
9 9

Equation at the end of step 2 :

(4xy + 54x) (18x - 7xy)
(——————————— - ———————————) + 2
9 3

Step 3 :

4xy+54x 18x-7xy
Simplify ——————— - ———————
9 3

Pulling out like terms :

3.1 Pull out like factors :

4xy + 54x = 2x • (2y + 27)
Pulling out like terms :

3.2 Pull out like factors :

18x - 7xy = -x • (7y - 18)
Calculating the Least Common Multiplier :

3.3 Find the Least Common Multiple (L.C.M)

The left denominator is : 9

The right denominator is : 3

Factor the left and right denominators, counting
the number of times each factor appears :

|———————————————|—————————————————————————————————————|
| | Number of times each prime factor |
| | appears the factorization of: |
| | |
| Prime | Left Right L.C.M = Max |
| Factors |Denominator Denominator {Left,Right}|
| —————————— |——————————— ——————————— ————————————|
| 3 | 2 1 2 |
|———————————————|—————————————————————————————————————|
|Product of all | |
| Prime Factors | 9 3 9 |
|———————————————|—————————————————————————————————————|

Least Common Multiple: 9

Calculating Multipliers :

Calculate multipliers for the two fractions

L.C.M
L. Multiplier = —————————————— = 1
L. Denominator


L.C.M
R. Multiplier = —————————————— = 3
R. Denominator

Making Equivalent Fractions :

3.5 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. 2x • (2y+27)
—————————————————— = ————————————
L.C.M 9

R. Mult. • R. Num. -x • (7y-18) • 3
—————————————————— = ————————————————
L.C.M 9

Adding fractions that have a common denominator :

3.6 Adding up the two equivalent fractions

2x • (2y+27) - (-x • (7y-18) • 3) 25xy
————————————————————————————————— = ————
9 9

Equation at the end of step 3 :

25xy
———— + 2
9

Step 4 :

25xy
Simplify ———— + 2
9

Rewriting the whole as an Equivalent Fraction :

4.1 Adding a whole to a fraction

Rewrite the whole as a fraction using 9 as the denominator :

2 2 • 9
2 = — = —————
1 9

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

25xy + 2 • 9 25xy + 18
———————————— = —————————
9 9

Final result :

25xy + 18
—————————
9

Answer 2

Did you copy it from somewhere on internet? lol... @Muzzack

Answer 3

nope

Answer 4

haha ok I "believe" you.

Does this help you though? @Calvinvd