Respuesta :
Answer:
[tex]\frac{1}{3x+52}[/tex]
Step-by-step explanation:
We begin with the expression
[tex]\frac{\frac{1}{x^2+51x+50} }{\frac{2}{x+50}+\frac{1}{x+1} }[/tex]
First, we can split this into the product of two fractions
[tex]\frac{1}{x^2+51x+50} *(\frac{1}{\frac{2}{x+50}+\frac{1}{x+1}} )[/tex]
Now, we can factor the denominator of the first fraction.
[tex]\frac{1}{(x+1)(x+50)} *(\frac{1}{\frac{2}{x+50}+\frac{1}{x+1}} )[/tex]
Next, we need to create a common denominator for the second fraction
[tex]\frac{2}{x+50}+\frac{1}{x+1}\\\\\frac{2}{x+50}*\frac{x+1}{x+1} +\frac{1}{x+1}*\frac{x+50}{x+50} \\\\\frac{2x+2}{(x+1)(x+50)} + \frac{x+50}{(x+1)(x+50)}\\\\ \frac{3x+52}{(x+1)(x+50)}[/tex]
Now to return this portion to the denominator of the second fraction.
[tex]\frac{1}{(x+1)(x+50)} *(\frac{1}{\frac{3x+52}{(x+1)(x+50)} } )[/tex]
Dividing by a fraction is the same as multiplying as the reciprocal of the fraction, so the second fraction becomes
[tex]\frac{1}{(x+1)(x+50)} *\frac{(x+1)(x+50)}{3x+52}[/tex]
Now to reduce this expression by canceling out [tex](x+1)(x+5)[/tex]
[tex]\frac{(x+1)(x+50)}{(x+1)(x+50)(3x+52)}\\\\\frac{1}{3x+52}[/tex]