Question

x+10/4 + x+3/3 = x+4/2​

Answer 1

Answer

Answer:

x = 5 Or x =

$\frac{5}{2}$

Explanation:

Given

$\frac{x-1}{x-2}+\frac{x-3}{x-4}=\frac{10}{3}</p><p>[tex]\implies \frac{(x-1)(x-4)+(x-3)(x-2)}{(x-2)(x-4)}=\frac{10}{3}$

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

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

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

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

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

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

Divide each term by 2 ,we get

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

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

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

Math

8 points

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

=

$\frac{5}{2}$

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