Question

solve for x where x is not equal to 3/2&5

Answer 1

[tex] \frac{1}{2x-3} + \frac{1}{x-5} =1 \frac{1}{9} \\ \frac{(x-5)+(2x-3)}{(2x-3)(x-5)} = \frac{10}{9} \\ (3x-8)(9)=10(2 x^{2} -10x -3x+15) \\ 27x-72=20 x^{2} -130x+150 \\ 20 x^{2} -130x-27x+150+72=0 \\ 20 x^{2} -157x+222=0 \\ 20 x^{2} -120x-37x+222=0 \\ 20x(x-6)-37(x-6)=0 \\ (20x-37)(x-6)=0 \\ x = \frac{37}{20} \ \ \ \ \ or \ \ \ \ \ 6[/tex]

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