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

`(x+1)/( x^(2) +x-6) / ( x^(2) +5x+4)/(x-2) \\ (x+1)/((x+3)(x-2)) / (x-2)/((x+1)(x+4)) \\ (x+1)/((x+3)(x-2))* ((x+1)(x+4))/(x-2) \\ (1)/((x+3)(x+4))`

Answer 2

Answer: The simplified form will be

`(1)/((x+3)(x+4))`

Explanation:

Since we have given that

`(x+1)/(x^2+x-6)/ (x^2+5x+4)/(x-2)`

We need to simplify the above expression, we get that

`(x+1)/(x^2+x-6)/ (x^2+5x+4)/(x-2)\\\\=(x+1)/(x^2+x-6)* (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

`(x+1)/(x^2+x-6)* (x-2)/(x^2+5x+4)\\\\=(x+1)/((x+3)(x-2))* (x-2)/((x+4)(x+1))\\\\=(1)/((x+3)(x+4))`

Hence, the simplified form will be

`(1)/((x+3)(x+4))`