Question

URGENT! PLEASE help me! Full solutions please, and no nonsense answers.

Answer 1

Answer:

$\frac{1}{3x+52}$

Step-by-step explanation:

Given

$\frac{\frac{1}{x^2+51x+50} }{\frac{2}{x+50}+\frac{1}{x+1} }$

= $\frac{\frac{1}{(x+50)(x+1)} }{\frac{2(x+1)+x+50}{(x+50)(x+1)} }$

= $\frac{1}{(x+50)(x+1)}$ × $\frac{(x+50)(x+1)}{2x+2+x+50}$ ← cancel (x + 50)(x + 1) on numerator/denominator

= $\frac{1}{3x+52}$

Answer 2

Answer:

$\Large\boxed{\sf \bf \ \ \dfrac{1}{3x+52} \ \ }$

Step-by-step explanation:

Hello, please consider the following.

We need to do something with that, right !?

           $\dfrac{\left(\dfrac{1}{x^2+51x+50\right)}}{\left(\dfrac{2}{x+50}+\dfrac{1}{x+1}\right)}$

What can we say from $x^2+51x+50$ ?

The sum of the zeroes is -51=(-1)+(-50) and the product is 50 = (-1) x (-50), so we can factorise. Let's do it !

$x^2+51x+50=x^2+50x+x+50=x(x+1)+50(x+1)=(x+1)(x+50)$

That's a pretty cool first result !

Now, let's play with the denominator.

$\dfrac{2}{x+50}+\dfrac{1}{x+1}\\\\\text{*** We put on the same denominator which is (x+1)(x+50) ***}\\\\=\dfrac{2(x+1)}{(x+50)(x+1)}+\dfrac{x+50}{(x+1)(x+50)}\\\\=\dfrac{2(x+1)+x+50}{(x+50)(x+1)}\\\\=\dfrac{2x+2+x+50}{(x+50)(x+1)}\\\\=\dfrac{3x+52}{(x+50)(x+1)}$

We are almost there.

Let's combine all these results together !

$\dfrac{\left(\dfrac{1}{x^2+51x+50\right)}}{\left(\dfrac{2}{x+50}+\dfrac{1}{x+1}\right)}\\\\\\=\dfrac{\left(\dfrac{1}{(x+1)(x+50)\right)}}{\left(\dfrac{3x+52}{(x+50)(x+1)}\right)}}\\\\\\=\large\boxed{\dfrac{1}{3x+52}}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you