What is \frac{x^{6}-24x^{4}+144x^{2}}{(x^{2}+4\sqrt{3}x+12)(x-2\sqrt{3})^{2}} equal to?
- A. x^{2} ✓
- B. x^{2}-2
- C. x^{2}+2\sqrt{3}
- D. x^{2}-2\sqrt{3}
Correct Answer: A. x^{2}
Explanation
The numerator is x^2(x^4-24x^2+144) = x^2(x^2-12)^2. The denominator expands as ((x+2\sqrt{3})(x-2\sqrt{3}))^2 = (x^2-(2\sqrt{3})^2)^2 = (x^2-12)^2. Cancelling (x^2-12)^2 yields x^2.
Related questions on Algebra
- If p + q + r = 0, then what is z^{\frac{p^2}{qr}} \times z^{\frac{q^2}{rp}} \times z^{\frac{r^2}{pq}} equal to ?
- What is the value of k for which (k^2 - 5k + 4)x^2 + (k^2 - 3k - 4)x + (k^2 - 4k) = 0 is an identity ?
- If \frac{a^2}{b^2 + c^2} = \frac{b^2}{c^2 + a^2} = \frac{c^2}{a^2 + b^2}, then what is the value of a^4 + b^4 + c^4 equal to ?
- If \frac{1}{x} = \frac{1}{p} + \frac{1}{q}, then what is \frac{pq}{p^2 - q^2}\left(\frac{x + p}{x - p} - \frac{x + q}{x - q}\right) equa...
- If (x - 5) is the HCF of x^2 - x - p and x^2 - qx - 10, then what is the value of (p + q) ?