Question

x minus 1 upon x minus b + x minus b upon x minus equals to upon B + b Upon A$x - a \div x - b \: + x - b \div x - a \: = a \div b + b \div a$

Answer 1

Given:

$\frac{x-a}{x-b}+\frac{x-b}{x-a}=\frac{a}{b}+\frac{b}{a}$

Explanation:

Let m = (x-a)/(x-b) ----(1)

Now , equation becomes,

m+1/m = a/b+b/a

=>m-a/b = b/a - 1/m

=> (mb-a)/b = (bm-a)/am

Do the cross multiplication, we get

=> am(mb-a) = b(bm-a)

=> abm²-a²m=b²m-ab

=> abm²-a²m-b²m+ab=0

=> am(bm-a)-b(bm-a)=0

=> (bm-a)(am-b)=0

=> bm-a = 0 Or am-b=0

=> m = a/b or m = b/a

(x-a)/(x-b)=a/b Or (x-a)(x-b)=b/a

=> b(x-a)=a(x-b) Or a(x-a)=b(x-b)

=> bx-ab=ax-ab or ax-a²=bx-b²

=> bx-ax=0 or ax-bx = a²-b²

=> x(b-a)=0 or x(a-b)=(a+b)(a-b)

=> x = 0 Or x = [(a+b)(a-b)]/(a-b)

=> x = 0 Or x = a+b

Therefore,

x = 0 or x = a+b

••..

Answer 2

Answer:

Step-by-step explanation:

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