Questions: Write the following as a single rational expression. Multiply (200+35 x)/x divided by (250+40 x)/x a.) (50+5 x)/x^2 b.) (250+40 x)/(200+35 x) c.) (40+7 x)/(50+8 x)

Write the following as a single rational expression. Multiply (200+35 x)/x divided by (250+40 x)/x a.) (50+5 x)/x^2 b.) (250+40 x)/(200+35 x) c.) (40+7 x)/(50+8 x)
Transcript text: Write the following as a single rational expression. Mul $\frac{200+35 x}{x} \div \frac{250+40 x}{x}$ a.) $\frac{50+5 x}{x^{2}}$ b.) $\frac{250+40 x}{200+35 x}$ c.) $\frac{40+7 x}{50+8 x}$
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Solution

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Solution Steps

Step 1: Understand the Problem

We are given two rational expressions and asked to divide them. The expressions are:

\[ \frac{200+35x}{x} \quad \text{and} \quad \frac{250+40x}{x} \]

We need to divide the first expression by the second and simplify the result.

Step 2: Division of Rational Expressions

To divide two rational expressions, we multiply the first expression by the reciprocal of the second expression. Therefore, we have:

\[ \frac{200+35x}{x} \div \frac{250+40x}{x} = \frac{200+35x}{x} \times \frac{x}{250+40x} \]

Step 3: Simplify the Expression

When multiplying the expressions, the \(x\) in the numerator and denominator cancel out:

\[ \frac{200+35x}{x} \times \frac{x}{250+40x} = \frac{200+35x}{250+40x} \]

Final Answer

The simplified rational expression is:

\[ \boxed{\frac{200+35x}{250+40x}} \]

This corresponds to option (b).

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