Dear student We have,3x4-18753x2-75=3x4-6253x2-25=x4-625x2-25=x22-252x2-25=x2-25x2+25x2-25 using a2-b2=a+ba-b=x2+25 Regards

(3x⁴-1875)/(3x²-75)

Dear student

We have, \frac{3 x^{4} - 1875}{3 x^{2} - 75} = \frac{3 (x^{4} - 625)}{3 (x^{2} - 25)} = \frac{x^{4} - 625}{x^{2} - 25} = \frac{{(x^{2})}^{2} - {(25)}^{2}}{x^{2} - 25} = \frac{(x^{2} - 25) (x^{2} + 25)}{x^{2} - 25} [using a^{2} - b^{2} = (a + b) (a - b)] = x^{2} + 25

Regards

(3x4-1875)/(3x2-75)