Questions: Adding rational expressions with different Subtract. [ frac74-frac53 d ] Simplify your answer as much as possible.

Adding rational expressions with different Subtract. [ frac74-frac53 d ] Simplify your answer as much as possible.
Transcript text: Adding rational expressions with different Subtract. \[ \frac{7}{4}-\frac{5}{3 d} \] Simplify your answer as much as possible. $\square$ Explanation Check
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Solution

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Solution Steps

To subtract rational expressions with different denominators, first find a common denominator. In this case, the common denominator is the product of the two denominators, \(4\) and \(3d\). Rewrite each fraction with the common denominator, then perform the subtraction. Finally, simplify the resulting expression if possible.

Step 1: Identify the Rational Expressions

We start with the rational expressions: \[ \frac{7}{4} - \frac{5}{3d} \]

Step 2: Find the Common Denominator

The common denominator for the fractions is \(12d\) (the product of \(4\) and \(3d\)). We rewrite each fraction: \[ \frac{7}{4} = \frac{7 \cdot 3d}{4 \cdot 3d} = \frac{21d}{12d} \] \[ \frac{5}{3d} = \frac{5 \cdot 4}{3d \cdot 4} = \frac{20}{12d} \]

Step 3: Perform the Subtraction

Now we can subtract the two fractions: \[ \frac{21d}{12d} - \frac{20}{12d} = \frac{21d - 20}{12d} \]

Step 4: Simplify the Result

The expression \(\frac{21d - 20}{12d}\) is already in its simplest form, as there are no common factors to reduce further.

Final Answer

The simplified result of the subtraction is: \[ \boxed{\frac{21d - 20}{12d}} \]

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