Math Snap

STEP 1

1. The problem involves adding two rational expressions.
2. The denominators $x-7$ and $7-x$ can be manipulated for simplification.
3. The goal is to simplify the expression.

STEP 2

1. Simplify the denominators.
2. Find a common denominator.
3. Combine the numerators over the common denominator.
4. Simplify the resulting expression.

STEP 3

Simplify the denominators. Notice that $7-x$ can be rewritten as $-(x-7)$.
$$\frac{3x-8}{x-7} + \frac{2x-1}{7-x} = \frac{3x-8}{x-7} - \frac{2x-1}{x-7}$$

STEP 4

Since the denominators are now the same, $x-7$, we can combine the fractions.
$$\frac{3x-8 - (2x-1)}{x-7}$$

STEP 5

Simplify the numerator by distributing and combining like terms.
$$3x - 8 - 2x + 1 = x - 7$$

The expression now becomes:
$$\frac{x-7}{x-7}$$ Simplify the fraction:
$$\frac{x-7}{x-7} = 1$$ The simplified expression is:
$$\boxed{1}$$