Home > Algebra calculators > Roots for Non-Zero Denominator calculator

 Solve any problem (step by step solutions) Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
 Problem: (4x+1)/(4x-1)+(4x-1)/(4x+1)=3 [ Calculator, Method and examples ]Solution:Your problem -> (4x+1)/(4x-1)+(4x-1)/(4x+1)=3(4x+1)/(4x-1)+(4x-1)/(4x+1)=3((4*x+1)/(4*x-1))+((4*x-1)/(4*x+1))=3Let (4*x+1)/(4*x-1)=m=>m+1/m=3=>m^2-3m+1=0=>m^2-3m+1 = 0factor is not possible for equation m^2-3m+1=0Solution is possible using the method of perfect square.Comparing the given equation with the standard quadratic equation ax^2+bx+c=0,we get, a=1, b=-3, c=1.:. Delta=b^2-4ac=(-3)^2-4 (1) (1)=9-4=5:. sqrt(Delta)=sqrt(5)Now, alpha=(-b+sqrt(Delta))/(2a)=(-(-3)+sqrt(5))/(2*1)=(3+sqrt(5))/2 and, beta=(-b-sqrt(Delta))/(2a)=(-(-3)-sqrt(5))/(2*1)=(3-sqrt(5))/2Now, (4*x+1)/(4*x-1)=(3+sqrt(5))/2=>(4*x+1)/(4*x-1)=2.62=>(4*x+1)=2.62(4*x-1)=>4x+1=10.47x-2.62=>4x-10.47x=-1-2.62=>6.47x = 3.62=>x = 3.62/6.47=>x = 0.56Now, (4*x+1)/(4*x-1)=(3-sqrt(5))/2=>(4*x+1)/(4*x-1)=0.38=>(4*x+1)=0.38(4*x-1)=>4x+1=1.53x-0.38=>4x-1.53x=-1-0.38=>2.47x = -1.38=>x = -1.38/2.47=>x = -0.56

Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me