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Perform the indicated operation and simplify the result. Leave your answer in factored form.

[tex]\[ \frac{x+3}{x-8} + \frac{6x-7}{x-8} \][/tex]

[tex]\[ \frac{x+3}{x-8} + \frac{6x-7}{x-8} = \square \][/tex]

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Sagot :

GinnyAnswer
Let's break down the given problem step-by-step to simplify the expression:

Given expressions:
[tex]\[ \frac{x+3}{x-8} + \frac{6x-7}{x-8} \][/tex]

Since the denominators are the same, we can directly add the numerators:
[tex]\[ \frac{(x+3) + (6x-7)}{x-8} \][/tex]

Next, combine the terms in the numerator:
[tex]\[ (x + 3) + (6x - 7) = x + 3 + 6x - 7 = 7x - 4 \][/tex]

So the expression simplifies to:
[tex]\[ \frac{7x - 4}{x-8} \][/tex]

This is already in its simplest form as the numerator \(7x - 4\) cannot be factored further to cancel with the denominator \(x - 8\).

Our final simplified result is:
[tex]\[ \frac{7x - 4}{x-8} \][/tex]
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