Simplify \(\frac{4}{x+1}-\frac{3}{x-1}\)
Question 1 Report
Simplify \(\frac{4}{x+1}-\frac{3}{x-1}\)
Answer Details
To simplify \(\frac{4}{x+1}-\frac{3}{x-1}\), we first need to find a common denominator for the two fractions. The common denominator is \((x+1)(x-1)\), so we can rewrite the expression as follows:
$$\frac{4(x-1)}{(x+1)(x-1)} - \frac{3(x+1)}{(x+1)(x-1)}$$
Next, we can combine the two fractions by subtracting the second fraction from the first, giving us:
$$\frac{4(x-1)-3(x+1)}{(x+1)(x-1)}$$
Simplifying the numerator, we get:
$$\frac{4x-4-3x-3}{(x+1)(x-1)} = \frac{x-7}{x^2-1}$$
Therefore, the answer is $\frac{x-7}{x^2-1}$
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