Question

solve for x and y , x-1 / x-2 + x-3 / x-4 = 10/3.​

Answer 1

Answer:

Answer:

$\underline{\boxed{\gray{\sf Given \: : }}}$

$\underline{\boxed{\purple{\sf\frac{x-1}{x-2}+\frac{x-3}{x-4}=\frac{10}{3} }}}$

$\underline{\boxed{\pink{\sf\implies \frac{(x-1)(x-4)+(x-3)(x-2)}{(x-2)(x-4)}=\frac{10}{3} }}}$

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

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

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

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

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

$\underline{\boxed{\pink{\sf \implies 4x^{2}-30x+50=0 }}}$

$\large\mapsto\boxed{\sf\green{Divide \: each \: term \: by \: 2 ,we \: get}}$

$\underline{\boxed{\red{\sf \implies 2x^{2}-15x+25=0}}}$

$\large\mapsto\boxed{\sf\orange{Splitting \: the \: middle \: term, \: we \: get:}}$

$\underline{\boxed{\green{\sf \implies 2x^{2}-10x-5x+25=0}}}$

$\underline{\boxed{\red{\sf \implies 2x(x-5)-5(x-5)=0 }}}$

$\underline{\boxed{\green{\sf \implies (x-5)(2x-5)=0 }}}$

$\underline{\boxed{\red{\sf\implies x-5 = 0 \: Or \: 2x-5 = 0 }}}$

$\underline{\boxed{\green{\sf \implies x = 5 \: Or \: x=\frac{5}{2} }}}$

$\huge\pink{\boxed{therefore,}}$

$\underline{\boxed{\blue{\sf x = 5 Or x = \frac{5}{2}25}}}$

Answer 2

Answer:

x-1/x-2. + x-3/ x-4 = (x-1) (x-4) +( x-3 ) (x-2) / (x- 2)(x-4) =x^2 --5x+4 +x^2—5x+6 / x^2 --6x +8= ( 2x^2 --10x+10)/x^2--6x+8 =10/3 ...