Questions: Add: (-4)/(x-1)+(-3)/(x+2)

Solution Steps

To add the two fractions, we need to find a common denominator. The common denominator for the fractions \(\frac{-4}{x-1}\) and \(\frac{-3}{x+2}\) is \((x-1)(x+2)\). Once we have the common denominator, we can rewrite each fraction with this denominator and then add the numerators.

To add the fractions \(\frac{-4}{x-1}\) and \(\frac{-3}{x+2}\), we first identify the common denominator, which is \((x-1)(x+2)\).

We rewrite each fraction with the common denominator: \[ \frac{-4}{x-1} = \frac{-4(x+2)}{(x-1)(x+2)} = \frac{-4x - 8}{(x-1)(x+2)} \] \[ \frac{-3}{x+2} = \frac{-3(x-1)}{(x-1)(x+2)} = \frac{-3x + 3}{(x-1)(x+2)} \]

Now we can add the two fractions: \[ \frac{-4x - 8}{(x-1)(x+2)} + \frac{-3x + 3}{(x-1)(x+2)} = \frac{(-4x - 8) + (-3x + 3)}{(x-1)(x+2)} = \frac{-7x - 5}{(x-1)(x+2)} \]

Final Answer