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(1/3x−3)+(−3/4x−5)

2 min read Jun 16, 2024
(1/3x−3)+(−3/4x−5)

Simplifying the Expression: (1/3x−3)+(−3/4x−5)

This article will guide you through simplifying the expression (1/3x−3)+(−3/4x−5). We'll break down the steps and explain the concepts involved.

Understanding the Expression

The expression contains two sets of parentheses, each representing a binomial. A binomial is a polynomial with two terms. In this case, the terms are:

  • 1/3x and -3 in the first binomial
  • -3/4x and -5 in the second binomial

Combining Like Terms

To simplify the expression, we need to combine like terms. Like terms are terms that have the same variable and exponent.

  • x terms: 1/3x and -3/4x
  • constant terms: -3 and -5

Step 1: Combining x terms:

  • Find a common denominator for 1/3 and -3/4: 12
  • Convert the fractions: (4/12)x + (-9/12)x = -5/12x

Step 2: Combining constant terms:

  • Simply add the constants: -3 + (-5) = -8

Final Simplified Expression

After combining the like terms, the simplified expression is:

-5/12x - 8

Therefore, (1/3x−3)+(−3/4x−5) simplifies to -5/12x - 8.

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