Evaluate
-\frac{74x^{2}}{25}-\frac{7}{4}
Expand
-\frac{74x^{2}}{25}-\frac{7}{4}
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-3x^{2}+\frac{1}{2}+\left(\frac{1}{5}x+\frac{3}{2}\right)\left(\frac{1}{5}x-\frac{3}{2}\right)
Use the distributive property to multiply -5 by \frac{3}{5}x^{2}-\frac{1}{10}.
-3x^{2}+\frac{1}{2}+\left(\frac{1}{5}x\right)^{2}-\frac{9}{4}
Consider \left(\frac{1}{5}x+\frac{3}{2}\right)\left(\frac{1}{5}x-\frac{3}{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square \frac{3}{2}.
-3x^{2}+\frac{1}{2}+\left(\frac{1}{5}\right)^{2}x^{2}-\frac{9}{4}
Expand \left(\frac{1}{5}x\right)^{2}.
-3x^{2}+\frac{1}{2}+\frac{1}{25}x^{2}-\frac{9}{4}
Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.
-\frac{74}{25}x^{2}+\frac{1}{2}-\frac{9}{4}
Combine -3x^{2} and \frac{1}{25}x^{2} to get -\frac{74}{25}x^{2}.
-\frac{74}{25}x^{2}-\frac{7}{4}
Subtract \frac{9}{4} from \frac{1}{2} to get -\frac{7}{4}.
-3x^{2}+\frac{1}{2}+\left(\frac{1}{5}x+\frac{3}{2}\right)\left(\frac{1}{5}x-\frac{3}{2}\right)
Use the distributive property to multiply -5 by \frac{3}{5}x^{2}-\frac{1}{10}.
-3x^{2}+\frac{1}{2}+\left(\frac{1}{5}x\right)^{2}-\frac{9}{4}
Consider \left(\frac{1}{5}x+\frac{3}{2}\right)\left(\frac{1}{5}x-\frac{3}{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square \frac{3}{2}.
-3x^{2}+\frac{1}{2}+\left(\frac{1}{5}\right)^{2}x^{2}-\frac{9}{4}
Expand \left(\frac{1}{5}x\right)^{2}.
-3x^{2}+\frac{1}{2}+\frac{1}{25}x^{2}-\frac{9}{4}
Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.
-\frac{74}{25}x^{2}+\frac{1}{2}-\frac{9}{4}
Combine -3x^{2} and \frac{1}{25}x^{2} to get -\frac{74}{25}x^{2}.
-\frac{74}{25}x^{2}-\frac{7}{4}
Subtract \frac{9}{4} from \frac{1}{2} to get -\frac{7}{4}.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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