Discuss the results. Can I add fractions that do not have same denominators? 4/3x -(5x+6)/6x^2

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You can perform the difference of the fractions only if they have the same denominator, hence, you need to bring the fractions to a common denominator, such that:

`(4*2x)/(6x^2) - (5x+6)/(6x^2) = (8x - (5x + 6))/(6x^2)`

Opening the brackets, yields:

`(8x - 5x - 6)/(6x^2) = (3x - 6)/(6x^2) `

`4/(3x) - (5x+6)/(6x^2) = (3(x - 2))/(6x^2) `

Reducing duplicate factors yields:

`4/(3x) - (5x+6)/(6x^2) = (x - 2)/(2x^2) `

`4/(3x) - (5x+6)/(6x^2) = 1/(2x) - 1/x^2`

Hence, evaluating the difference of fractions yields `4/(3x) - (5x+6)/(6x^2) = 1/(2x) - 1/x^2.`

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Of course!

Beforre adding the fractions, we'll calculate the least common denominator.

In this case, LCD is:

LCD = 6x^2 (could be divided by 3x)

We'll multiply each fraction by LCD:

4*6x^2/3x - (5x+6)*6x^2/6x^2

We'll simplify and we'll get:

8x - (5x + 6)

We'll remove the brackets;

8x - 5x - 6

We'll combine like terms:

3x - 6

We'll factorize by 3 and we'll get the final result:

3(x-2)

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