Question

What is the simplified form of x plus 1 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x minus 2

Answer 1

Answer: The simplified form will be

$\frac{1}{(x+3)(x+4)}$

Step-by-step explanation:

Since we have given that

$\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}$

We need to simplify the above expression, we get that

$\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}\\\\=\frac{x+1}{x^2+x-6}\times \frac{x-2}{x^2+5x+4}$

Now, we first factorize the quadratic equation:

$x^2+x-6\\\\=x^2+3x-2x-6\\\\=x(x+3)-2(x-3)\\\\=(x+3)(x-2)$

Similarly,

$x^2+5x+4\\\\=x^2+4x+x+4\\\\=x(x+4)+1(x+4)\\\\=(x+4)(x+1)$

So, it will become

$\frac{x+1}{x^2+x-6}\times \frac{x-2}{x^2+5x+4}\\\\=\frac{x+1}{(x+3)(x-2)}\times \frac{x-2}{(x+4)(x+1)}\\\\=\frac{1}{(x+3)(x+4)}$

Hence, the simplified form will be

$\frac{1}{(x+3)(x+4)}$

Answer 2

$\frac{x+1}{ x^{2} +x-6} / \frac{ x^{2} +5x+4}{x-2} \\ \frac{x+1}{(x+3)(x-2)} / \frac{x-2}{(x+1)(x+4)} \\ \frac{x+1}{(x+3)(x-2)}* \frac{(x+1)(x+4)}{x-2} \\ \frac{1}{(x+3)(x+4)}$