Question

Which expression is equivalent to if no denominator equals zero

Answer 1

Answer:

B (1/x^2 - 4x + 3)

Step-by-step explanation:

You can first write the second equation as multiplication by multiplying by the reciprocal and then expand.

Answer 2

The result of the given division expression is $\frac{1}{(x-3)(x-1)}$

Given the expression;

• $\frac{x+3}{x^2-2x-3} + \frac{x^2+2x-3}{x+1}$

Factorize the quadratic function in the expression to have:

$=\frac{x+3}{x^2-3x+x-3} \div \frac{x^2+3x-x-3}{x+1} \\=\frac{x+3}{x(x-3)+1(x-3)} \div \frac{x(x+3)-1(x+3)}{x+1} \\=\frac{x+3}{(x-3)(x+1)} \div \frac{(x+3)(x-1)}{x+1} \\=\frac{x+3}{(x-3)(x+1)} \times \frac{x+1}{(x+3)(x-1)} \\=\frac{1}{(x-3)(x-1)}$

Hence the result of the given division expression is $\frac{1}{(x-3)(x-1)}$

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