How do you solve the rational equation #a/(a+5) = 3/(a+1)#?

2 Answers
May 29, 2018

Answer:

#a=-3, a=5#

Explanation:

#a/(a+5) = 3/(a+1)#

cross multiply:

#a(a+1) = 3(a+5)#

#a^2+a = 3a+15#

#a^2-2a -15= 0#
#(a+3)(a-5)= 0#

#a=-3, a=5#

May 29, 2018

Answer:

#a=-3" or "a=5#

Explanation:

#"multiply through by "(a+5)(a+1)#

#cancel((a+5))(a+1)xxa/cancel(a+5)=(a+5)cancel((a+1))xx3/cancel(a+1)#

#a(a+1)=3(a+5)larrcolor(blue)"distribute"#

#a^2+a=3a+15#

#"rearrange in "color(blue)"standard form ";ax^2+bx+c=0#

#"subtract "3a+15" from both sides"#

#a^2-2a-15=0#

#"the factors of - 15 which sum to - 2 are - 5 and + 3"#

#(a-5)(a+3)=0#

#"equate each factor to zero and solve for a"#

#a+3=0rArra=-3#

#a-5=0rArra=5#