if b-(b-x) = a-ax ,show that x = a-b
Answers
Step-by-step explanation:
The value of x is 2/( a+b-ab)
Step-by-step explanation:
Given Data: a/(ax-1) + b/(bx-1) = a+b ; To find the value of x:
a/ax-1 + b/bx-1 = a+b
Step 1:
(abx - a +abx-b)/(ax-1)(bx-1) = a+b
2 a b x-a-b=(a+b)\left(a b x^{2}-a x-b x+1\right)2abx−a−b=(a+b)(abx
2
−ax−bx+1)
Step 2:
2 \mathrm{abx}-\mathrm{a}-\mathrm{b}=\mathrm{a}^{2} \mathrm{bx}^{2}-\mathrm{a}^{2} \mathrm{x}-\mathrm{abx}+\mathrm{a}+\mathrm{ab}^{2} \mathrm{x}^{2}-\mathrm{abx}-\mathrm{b}^{2} \mathrm{x}+\mathrm{b}2abx−a−b=a
2
bx
2
−a
2
x−abx+a+ab
2
x
2
−abx−b
2
x+b
Step 3:
\begin{gathered}\left.\begin{array}{l}{x\left(2 a b-a^{2} b+a^{2}-a b^{2}+b^{2}\right)=2 a+2 b} \\ {x\left[(a+b)^{2}-a^{2} b-a b^{2}\right]=2 a+2}\end{array} \quad \text { (therefore, }(a+b)^{2}=a^{2}+b^{2}+2 a b\right)\end{gathered}
x(2ab−a
2
b+a
2
−ab
2
+b
2
)=2a+2b
x[(a+b)
2
−a
2
b−ab
2
]=2a+2
(therefore, (a+b)
2
=a
2
+b
2
+2ab)
Step 4:
x = 2(a+b)/(a+b)(a+b-ab) (cancelling a+b)
x = 2/( a+b-ab)