Write the following as a single rational expression. $$ \frac{200+35 x}{x}+\frac{250+40 x}{x} $$ a.) $$ \frac{50+5 x}{x^{2}} $$ b.) $$ \frac{5(10+x)}{x^{2}} $$ c.) $$ \frac{40+7 x}{50+8 x} $$ d.) $$ \frac{250+40 x}{200+35 x} $$

Question

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Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(200+35x\right)}{x}+\frac{\left(250+40x\right)}{x}$$
- step1: Remove the parentheses:
  $$\frac{200+35x}{x}+\frac{250+40x}{x}$$
- step2: Transform the expression:
  $$\frac{200+35x+250+40x}{x}$$
- step3: Add the terms:
  $$\frac{450+75x}{x}$$
Calculate or simplify the expression $$ 450+75*x $$.
Simplify the expression by following steps:
- step0: Solution:
  $$450+75x$$
To combine the two rational expressions $$ \frac{200+35x}{x} $$ and $$ \frac{250+40x}{x} $$, we can follow these steps:

1. **Identify a common denominator**: The common denominator for both fractions is $$ x $$.

2. **Combine the numerators**: Since both fractions have the same denominator, we can add the numerators directly:
   $$
   \frac{200 + 35x + 250 + 40x}{x}
   $$

3. **Simplify the numerator**: Combine like terms in the numerator:
   $$
   200 + 250 + 35x + 40x = 450 + 75x
   $$

4. **Write the combined expression**: The combined expression is:
   $$
   \frac{450 + 75x}{x}
   $$

Now, we can simplify this expression further. The numerator $$ 450 + 75x $$ can be factored:
$$
450 + 75x = 75(6 + x)
$$

Thus, the expression becomes:
$$
\frac{75(6 + x)}{x}
$$

This is not one of the options provided, so let's check if we can express it in a different form.

The final rational expression is:
$$
\frac{75(6 + x)}{x}
$$

None of the options a, b, c, or d match this expression directly. However, if we look at option b:
$$
\frac{5(10+x)}{x^2}
$$
we can see that it is not equivalent to our result.

Therefore, the correct answer is not listed among the options provided. The combined expression is:
$$
\frac{450 + 75x}{x}
$$ or equivalently $$\frac{75(6 + x)}{x}$$.
The combined expression is $$ \frac{450 + 75x}{x} $$, which simplifies to $$ \frac{75(6 + x)}{x} $$. None of the provided options match this result.

Write the following as a single rational expression.

a.)
b.)
c.)
d.)

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