(i) (6)/(5)x^(2)-(4)/(5)x^(3)+(5)/(6)+(3)/(2)x From (x^(3))/(3)-(5)/(2)x^(2)+(3)/(5)x(1)/(4)

Suzhoumeite

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Jun 03, 2024

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Simplifying Algebraic Expressions

In this article, we will explore the process of simplifying algebraic expressions, specifically focusing on the given expression:

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

Subtracting Another Expression

We are given another expression to subtract from the above expression:

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

Our goal is to simplify the resulting expression by combining like terms.

Step 1: Subtract the Expressions

To subtract the two expressions, we will perform the following operations:

(6)/(5)x^(2) - (4)/(5)x^(3) + (5)/(6) + (3)/(2)x - [(x^(3))/(3) - (5)/(2)x^(2) + (3)/(5)x + (1)/(4)]

Step 2: Combine Like Terms

First, let's combine the terms with the variable x^(3):

(-4)/(5)x^(3) - (1)/(3)x^(3) = (-7)/(15)x^(3)

Next, let's combine the terms with the variable x^(2):

(6)/(5)x^(2) + (5)/(2)x^(2) = (37)/(10)x^(2)

Now, let's combine the terms with the variable x:

(3)/(2)x - (3)/(5)x = (11)/(10)x

Finally, let's combine the constant terms:

(5)/(6) - (1)/(4) = (13)/(12)

Simplified Expression

After combining like terms, we are left with the simplified expression:

(37)/(10)x^(2) - (7)/(15)x^(3) + (11)/(10)x + (13)/(12)

And that's it! We have successfully simplified the given expressions.