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How do you solve #2/(x-1) - 2/3 =4/(x+1)#?

Answer 1

Savannah Anderson

#x = -5 or 2#

#2/(x-1) - 2/3 = 4/(x+1)#

#=># #2/(x-1)-4/(x+1)=2/3#

#implies# #(2(x+1)-4(x-1))/((x-1)*(x+1)) = 2/3#

#implies# #(2(x+1)-4(x-1))/(x^2-1) = 2/3#

#implies# #(6-2x)3 = 2(x^2-1)# #implies# #(3-x)3=x^2-1# #implies##x^2+3x-10=0#

[ solution of a general quadratic equation of the form #ax^2+bx+c=0# is given by #x=(-b+-sqrt(b^2-4ac))/(2a)#]

#implies# #x= (-3+-sqrt(9+40))/2# #implies##x = (-3+-7)/2# #implies##x = -5, 2#

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Answer 2

Eva Abramson

To solve the equation 2/(x-1) - 2/3 = 4/(x+1), we can follow these steps:

Multiply every term in the equation by the least common denominator (LCD) of (x-1), 3, and (x+1), which is 3(x-1)(x+1). This step eliminates the denominators.
Simplify the equation by distributing and combining like terms.
Solve for x by isolating the variable on one side of the equation.

The solution to the equation is x = -5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.