Questions: Simplify and reduce to a fraction 10x/(5x+3)-(0x-6)/(5x+3)=(10x+)/(5x+3)

$Simplify and reduce to a fraction 10x/(5x+3)-(0x-6)/(5x+3)=(10x+)/(5x+3)$

Transcript text: Simplify and reduce to a fraction \[ \frac{10 x}{5 x+3}-\frac{0 x-6}{5 x+3}=\frac{10 x+}{5 x+3} \]

Solution

Solution Steps

To simplify and reduce the given expression to a fraction, we need to combine the fractions by finding a common denominator and then simplifying the resulting expression.

Solution Approach

Identify the common denominator for the fractions.
Combine the numerators over the common denominator.
Simplify the resulting expression.

Step 1: Identify the Common Denominator

The common denominator for the fractions $\frac{10x}{5x+3}$ and $\frac{-6}{5x+3}$ is $5x + 3$.

Step 2: Combine the Numerators

Combine the numerators over the common denominator: \[ \frac{10x}{5x+3} - \frac{-6}{5x+3} = \frac{10x + 6}{5x+3} \]

Step 3: Simplify the Expression

Simplify the resulting fraction: \[ \frac{10x + 6}{5x + 3} \]

Step 4: Further Simplification

Notice that the numerator $10x + 6$ and the denominator $5x + 3$ do not have any common factors other than 1. Therefore, the fraction cannot be simplified further.

Final Answer

\[ \boxed{\frac{10x + 6}{5x + 3}} \]

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