Question 117953
{{{2/(p+5)+3/(p+1)}}} Start with the given expression




In order to combine these rational expressions, we need to have a common denominator

So we need to get the denominators to the LCD {{{(p+5)(p+1)}}}



 {{{((p+1)/(p+1))(2/(p+5))+3/(p+1)}}}  Multiply the 1st term by {{{(((p+1))/((p+1)))}}}. This will make the 1st term have a common denominator of {{{(p+5)(p+1)}}}


 {{{2(p+1)/(p+1)(p+5)+3/(p+1)}}} Combine the fractions


 {{{(2p+2)/(p+1)(p+5)+3/(p+1)}}} Distribute
 

 {{{(2p+2)/(p+1)(p+5)+((p+5)/(p+5))(3/(p+1))}}}  Multiply the 2nd term by {{{(((p+5))/((p+5)))}}}. This will make the 2nd term have a common denominator of {{{(p+5)(p+1)}}}



 {{{(2p+2)/(p+1)(p+5)+3(p+5)/(p+1)(p+5)}}}  Combine the fractions



 {{{(2p+2)/(p+1)(p+5)+(3p+15)/(p+1)(p+5)}}}  Distribute




 {{{((2p+2)+(3p+15))/(p+1)(p+5)}}}  Since every fraction has the common denominator {{{(p+5)(p+1)}}}, we can combine them




 {{{(5p+17)/(p+1)(p+5)}}} Combine like terms




So {{{2/(p+5)+3/(p+1)}}} simplifies to  {{{(5p+17)/(p+1)(p+5)}}}