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Chapter 5: Problem 22

Simplify \(\frac{2 x-5}{10}-\frac{3 x-2}{15}\)

Short Answer

Expert verified
Question: Simplify the expression: \(\frac{2x - 5}{10} - \frac{3x - 2}{15}\) Answer: \(\frac{-11}{30}\)

Step by step solution

01

Find the least common multiple (LCM) of the denominators

To combine the two fractions, we first need to find a common denominator. In this exercise, the denominators are 10 and 15. The least common multiple (LCM) of 10 and 15 is 30. This is the smallest number that both 10 and 15 evenly divide into.
02

Rewrite both fractions with a common denominator

Now that we have the common denominator (30), we will rewrite both fractions with the denominator of 30. To do this, we multiply the numerator and denominator of each fraction by the necessary factor to make the denominator 30: \(\frac{2x - 5}{10} \cdot \frac{3}{3} = \frac{6x - 15}{30}\) \(\frac{3x - 2}{15} \cdot \frac{2}{2} = \frac{6x - 4}{30}\)
03

Combine the fractions

With both fractions rewritten with a common denominator, we can now combine them: \(\frac{6x - 15}{30} - \frac{6x - 4}{30} = \frac{(6x - 15) - (6x - 4)}{30}\)
04

Simplify the numerator

Now, we'll simplify the numerator by combining like terms: \((6x - 15) - (6x - 4) = 6x - 15 - 6x + 4 = 0x - 11 = -11\)
05

Write the final simplified expression

Lastly, we can write the final simplified expression based on the new numerator and denominator, which is: \(\frac{-11}{30}\)

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Most popular questions from this chapter

Find the value of \(5(8+3)-2(-3-6)\).

Express as simply as possible: (a) \(7 \times x \times 4 \times 2 \times y\) (b) \(-8 \times 2 \times a \times b\) (c) \(2 \times x \times 3 \times y \times 4 z\)

Find \(\frac{8}{5}\) of 120

In each case, simplify the given expression, if possible. \( x^{2}+3 x+1\)

Write down the reciprocal of the following: (a) \(\frac{1}{3}+\frac{1}{2}\) (b) \(\frac{x+y}{13}\) (c) \(\frac{2 R+1}{R-1}\) (d) \(4 !\)
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