Question

y : (" align="absmiddle" class="latex-formula">+$\frac{3}{36}$+$\frac{3}{60}$+...+$\frac{3}{29700}$) = $\frac{1}{14}$+$\frac{1}{35}$+$\frac{1}{65}$+...+$\frac{1}{350}$

Answer 1

Answer:

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

2

5

Explanation:

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

x−2

x−1

+

x−4

x−3

=

3

10

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

(x−2)(x−4)

(x−1)(x−4)+(x−3)(x−2)

=

3

10

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

x

2

−4x−2x+8

x

2

−4x−x+4+x

2

−2x−3x+6

=

3

10

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

x

2

−6x+8

2x

2

−10x+10

=

3

10

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

2

−10x+10)=10(x

2

−6x+8)

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

2

−30x+30=10x

2

−60x+80

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

2

−60x+80−6x

2

+30x−30

\implies 4x^{2}-30x+50=0⟹4x

2

−30x+50=0

Divide each term by 2 ,we get

\implies 2x^{2}-15x+25=0⟹2x

2

−15x+25=0

Splitting the middle term,we get

\implies 2x^{2}-10x-5x+25=0⟹2x

2

−10x−5x+25=0

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

\implies (x-5)(2x-5)=0⟹(x−5)(2x−5)=0

\implies x-5 = 0 \: Or \: 2x-5 = 0⟹x−5=0Or2x−5=0

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

2

5

Therefore,

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

2

5

••••

Answer 2

Answer:

whats the given?? what you need I don't understand