To find an expression equivalent to [tex]\(\frac{200}{x} - \frac{500}{7x}\)[/tex], let's go through the steps to combine these fractions carefully:
1. Identify a common denominator:
- Both fractions have [tex]\(x\)[/tex] in the denominator. The fractions can be expressed as [tex]\(\frac{a}{bx}\)[/tex] where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are numbers. Here, the denominators are [tex]\(x\)[/tex] and [tex]\(7x\)[/tex].
2. Rewrite each fraction with the common denominator:
- The common denominator is [tex]\(7x\)[/tex]. To rewrite [tex]\(\frac{200}{x}\)[/tex] with this common denominator, we need to multiply both the numerator and the denominator by 7:
[tex]\[
\frac{200}{x} = \frac{200 \cdot 7}{x \cdot 7} = \frac{1400}{7x}
\][/tex]
3. Subtract the second fraction from the rewritten first fraction:
- Now that both fractions have the same denominator, we can combine them:
[tex]\[
\frac{1400}{7x} - \frac{500}{7x}
\][/tex]
4. Combine the fractions by subtracting the numerators:
- Subtract the numerator of the second fraction from the numerator of the first fraction:
[tex]\[
\frac{1400 - 500}{7x} = \frac{900}{7x}
\][/tex]
The equivalent expression that we get is:
[tex]\[
\frac{900}{7x}
\][/tex]
Therefore, the correct option is:
C. [tex]\(\frac{900}{7x}\)[/tex]
