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 plus 4 ?

Answer 1

Answer:

Option B is correct.

Step-by-step explanation:

We have given an expression:

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

After rearranging the terms from $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}$

We will get $\frac{(x+1)(x+4)}{(x^2+x-6)(x^2+5x+4)}$

Now, we will simplify the terms

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

After further simplification we will get

$\frac{(x+4)(x+1)}{(x(x+3)-2(x+3))(x(x+4)+1(x+4))}$

Now,  we will get

$\frac{(x+4)(x+1)}{(x-2)(x+3)(x+1)(x+4)}$

Now, cancel out the common terms from numerator and denominator which is (x+4)(x+1) we will get

$\frac{1}{(x-2)(x+3)}$

Therefore, Option B is correct.

Answer 2

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

       x +1                  1                     1
= ---------------- * ----------- = ------------------
    (x +3)(x -2)     ( x +1)       (x +3)(x -2)

so the second choice is right sure