Divide the numerator and denominator by ab

\(\frac{\frac{b(a+b)}{ab}(\frac{b}{a}-1)}{\frac{a(a-b)}{ab}(\frac{a}{b}-1)}\)


\(\frac{\frac{(a+b)}{a}(\frac{b}{a}-1)}{\frac{(a-b)}{b}(\frac{a}{b}-1)}\)


\(\frac{(1+\frac{b}{a})(\frac{b}{a}-1)}{(\frac{a}{b}-1)(\frac{a}{b}-1)}\)


\(\frac{(\frac{b}{a}+1)(\frac{b}{a}-1)}{(\frac{a}{b}-1)(\frac{a}{b}-1)}\)


\(\frac{(\frac{b}{a})^2-1}{(\frac{a}{b}-1)^2}\)

Now substitute the value a/b=2/5 and b/a = 5/3

\(\frac{(\frac{5}{3})^2-1}{(\frac{3}{5}-1)^2}\)


\(\frac{\frac{25}{9}-1}{(\frac{-2}{5})^2}\)


\(\frac{\frac{16}{9}}{\frac{4}{25}}\)


\((\frac{16}{9})(\frac{25}{4})\)


\(\frac{100}{9}\)

Great Job

more effeient wy to do it ??

Since there can be only ONE possible answer to this question, we can replace a and b with 3 and 5 respectively to get:

\(\frac{b(a+b)(\frac{b}{a}-1)}{a(a-b)(\frac{a}{b}-1)}=\frac{5(3+5)(\frac{5}{3}-1)}{3(3-5)(\frac{3}{5}-1)}\)

\(=\frac{5(8)(\frac{2}{3})}{3(-2)(-\frac{2}{5})}\)

\(=\frac{\frac{80}{3}}{\frac{12}{5}}\)

\(=\frac{80}{3} \times \frac{5}{12}\)

\(=\frac{400}{36}\)

\(=\frac{100}{9}\)


Answer: \(\frac{100}{9}\)

please help me where m i going wrong as i get answer as 4.
i rewrote the terms as :
b/a * a+b/a-b*(b/a-1)/(a/b-1)
5/3*{ a+b/a-b}*(5/3-1)/(3/5-1)
5/3*{a+b/a-b}*(2/3*5/-2)

since all numbers divide each other we get
-1 *{a+b/a-b}
-1{ (8b/5)/-2b/5}
-1 *{-4}
4



= 4
-1 * {(3b/5) +b / (3b/5) -b}

check this line 5/3*{ a+b/a-b}*(5/3-1)/(3/5-1)

(3/5-1)=(-2/5) but you took (5/-2)

yes ,
3/5 -1 = -2 /5 ,
so, in above equation , we divide (2/3) / (-2 /5),
we can rewrite it as (2/3) * (5/-2).
kindly answer.
thanx.

(2/3) * (5/-2)=(-5/3)

=5/3*{a+b/a-b}*(-5/3)

=(-25/9)*(((a/b)+1/(a/b)-1))

=(-25/9)*(((3/5)+1/(3/5)-1))

=(-25/9)*((8/5)/(-2/5))

=(-25/9)*(-4)

=100/9

answer is 100/9

thanks, got it!

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