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\frac{\left(4x^{4}+3x^{3}\right)\times 2x^{2}}{2x^{2}}-\frac{1}{2x^{2}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{4}+3x^{3} times \frac{2x^{2}}{2x^{2}}.
\frac{\left(4x^{4}+3x^{3}\right)\times 2x^{2}-1}{2x^{2}}
Since \frac{\left(4x^{4}+3x^{3}\right)\times 2x^{2}}{2x^{2}} and \frac{1}{2x^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{8x^{6}+6x^{5}-1}{2x^{2}}
Do the multiplications in \left(4x^{4}+3x^{3}\right)\times 2x^{2}-1.