Question

x-1/x-2 +x-3/x-4=10/3​

Answer 1

Answer:

hey

x = 5 Or x = \frac{5}{2}

Explanation:

Given \frac{x-1}{x-2}+\frac{x-3}{x-4}=\frac{10}{3}

\implies \frac{(x-1)(x-4)+(x-3)(x-2)}{(x-2)(x-4)}=\frac{10}{3}

\implies \frac{x^{2}-4x-x+4+x^{2}-2x-3x+6}{x^{2}-4x-2x+8}=\frac{10}{3}

\implies \frac{2x^{2}-10x+10}{x^{2}-6x+8}=\frac{10}{3}

\implies 3(2x^{2}-10x+10)=10(x^{2}-6x+8)

\implies 6x^{2}-30x+30=10x^{2}-60x+80

\implies 0= 10x^{2}-60x+80-6x^{2}+30x-30

\implies 4x^{2}-30x+50=0

Divide each term by 2 ,we get

\implies 2x^{2}-15x+25=0

Splitting the middle term,we get

\implies 2x^{2}-10x-5x+25=0

\implies 2x(x-5)-5(x-5)=0

\implies (x-5)(2x-5)=0

\implies x-5 = 0 \: Or \: 2x-5 = 0

\implies x = 5 \: Or \: x=\frac{5}{2}

Therefore,

x = 5 Or x = \frac{5}{2}