Question

Solve the following:
$\frac{a^3-a-2b-\frac{b^2}{a}}{(1-\sqrt{\frac{1}{a}+\frac{b}{a^2}})(a+\sqrt{a+b})}:(\frac{a^3+a^2+ab+a^{2}b}{a^2-b^2}+\frac{b}{a-b})$ for $a=23,b=22$

Answer 1

Put the value of $a$ and $b$ in the given expression.

We have ,

$\frac{{23}^3-23-(2\times 22)-\frac{{22}^2}{23}}{(1-\sqrt{\frac{1}{23}+\frac{22}{{23}^2}})(a+\sqrt{22+23})}:$ $(\frac{{23}^3+{23}^2+23\times 22+{23}^2\times 22}{{23}^2-{22}^2}+\frac{22}{23-22})$

Now simplify the expression,

$\frac{\frac{({23}^4-{23}^2-(2\times 23\times 22)-{22}^2)(23-\sqrt{23+22})}{23}}{\left(\frac{23-\sqrt{{23}^2+22}}{23}\right)(23+\sqrt{23+22})(23-\sqrt{23+22})}:$ $\frac{{23}^3+{23}^2+(23\times 22)+({23}^2\times 22)+22(23+22)}{{23}^2-{22}^2}$

$\frac{\frac{\left(277816\right)(23-\sqrt{45}}{23}}{\frac{(23-\sqrt{45)}(529-45)}{23}}:$ $\frac{25370}{45}$

$\frac{\left(277816\right)(23+\sqrt{45})}{23}\times \frac{23}{(23-\sqrt{45})\left(484\right)}:\frac{25370}{45}$

$\frac{277816}{484}$:$\frac{25370}{45}$

$\frac{277816}{484}\times \frac{45}{25370}=1.0181316$ hence this the final answer.