How do you solve #1/(2(x-3))+3/(2-x)=5 x#?

Question

Avery Alexander · Accepted Answer

# x = 1.436#
and
#x = 3.064# #1/(2(x-3))+3/(2-x)=5 x# Make the denominators equal: #1/(2(x-3)) xx(2-x)/(2-x) +3/(2-x) xx (2(x-3))/(2(x-3))=5 x# #(2-x)/(2(x-3)(2-x)) + (3xx2(x-3))/(2(x-3)(2-x) =5# Now we can add the numerators: #=>( (2-x) + 6(x-3))/(2(x-3)(2-x)) =5# # (2-x +6x-18)/(2(x-3)(2-x)) =5# Transposition : # => (2-x +6x-18) = 5xx2(x-3)(2-x)# #=> 5x -16 = 10(x(2-x) -3(2-x)# #=> 5x -16 = 10(2x-x^2 -6+ 3x)# #=> 5x -16 = 10(5x-x^2 -6)# #=> 5x -16 = 50x-10x^2 -60# #=> 50x-5x-10x^2 -60+16 = 0# #=> -10x^2 +45x -44 =0# #= 10x^2 -45x+ 44 = 0# Solve using quadratic formula: #x=( -b +-sqrt(b^2 -4ac))/(2a)# Here# a= 10, b= -45 and c= 44# #b^2 -4ac = 2025-1760 = 265# We get : # x = 1.436# or #x = 3.064#

Savannah Anderson · Answer

undefined To solve the equation 1/(2(x-3))+3/(2-x)=5x, we can follow these steps:

1. Find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is (2(x-3))(2-x).

2. Multiply each term by the common denominator to eliminate the fractions.

3. Simplify the equation by distributing and combining like terms.

4. Rearrange the equation to isolate the variable x.

5. Solve for x by applying the appropriate algebraic operations.

The final solution will be the value(s) of x that satisfy the equation.