Questions: (63m+9)/(7m-6)+(63)/(6-7m)

Solution Steps

To solve the given expression, we need to simplify the addition of two fractions. Notice that the second fraction has a denominator that is the negative of the first fraction's denominator. This means we can rewrite the second fraction to have a common denominator with the first. After rewriting, we can add the fractions directly. Simplify the resulting expression if possible.

We start with the expression: \[ \frac{63m + 9}{7m - 6} + \frac{63}{6 - 7m} \] Notice that the second fraction can be rewritten as: \[ \frac{63}{6 - 7m} = -\frac{63}{7m - 6} \] Thus, we can express the entire equation as: \[ \frac{63m + 9}{7m - 6} - \frac{63}{7m - 6} \]

Now that both fractions have a common denominator, we can combine them: \[ \frac{(63m + 9) - 63}{7m - 6} \] This simplifies to: \[ \frac{63m + 9 - 63}{7m - 6} = \frac{63m - 54}{7m - 6} \]

Next, we can factor out the numerator: \[ 63m - 54 = 9(7m - 6) \] Thus, we have: \[ \frac{9(7m - 6)}{7m - 6} \] Assuming \(7m - 6 \neq 0\), we can cancel the common terms: \[ 9 \]

Final Answer