How do you solve #10/(x + 4) = 15/(4x + 4)# and find any extraneous solutions?

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Answer 1 · 2017-11-20T11:23:18

Solution: # x= 4/5#

#10/(x+4)=15/(4x+4)# Multiplying by #(x+4)(4x+4)# on

both sides we get #10(4x+4)=15(x+4) # or

#40x+40=15x+60 :. 25x =20 or x = 20/25= 4/5#

Check: L.H.S #=10/(x+4)=10/(4/5+4)= 10/(24/5)=50/24=25/12#

R.H.S #=15/(4x+4)=15/(4*4/5+4)= 15/(16/5+4)=15/(36/5)=75/36#

#25/12 :. # L.H.S #=# R.H.S . No invalid solution to original

problem so there is no extraneous solution.

Solution: # x= 4/5# [Ans]