Questions: Subtract the rational expressions. Reduce the final answer. 47/(2h-8) - 4/(h-4)

Solution Steps

To subtract the rational expressions, we need to find a common denominator. The denominators are \(2h - 8\) and \(h - 4\). Notice that \(2h - 8\) can be factored as \(2(h - 4)\). Thus, the common denominator is \(2(h - 4)\). Rewrite each fraction with the common denominator and then subtract the numerators. Finally, simplify the resulting expression if possible.

We start with the rational expressions: \[ \frac{47}{2h - 8} - \frac{4}{h - 4} \]

The denominators are \(2h - 8\) and \(h - 4\). We can factor \(2h - 8\) as \(2(h - 4)\). Thus, the common denominator is: \[ 2(h - 4) \]

We rewrite the first expression: \[ \frac{47}{2(h - 4)} = \frac{47}{2h - 8} \] For the second expression, we multiply the numerator and denominator by 2 to match the common denominator: \[ \frac{4}{h - 4} = \frac{8}{2(h - 4)} \]

Now we can subtract the two expressions: \[ \frac{47}{2(h - 4)} - \frac{8}{2(h - 4)} = \frac{47 - 8}{2(h - 4)} = \frac{39}{2(h - 4)} \]

The simplified result is: \[ \frac{39}{2(h - 4)} \]

Final Answer