$\text{a)}f\left(x\right)+g\left(x\right)=\frac{3}{4}{x}^6-2x^4+\frac{5}{4}{x}^2+4+\frac{1}{4}{x}^6+2x^4+x^3-\frac{1}{4}{x}^2-2x+2=x^6+x^3+x^2-2x+6$  

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$f\left(x\right)-g\left(x\right)=\left(\frac{3}{4}{x}^6-2x^4+\frac{5}{4}{x}^2+4\right)-\left(\frac{1}{4}{x}^6+2x^4+x^3-\frac{1}{4}{x}^2-2x+2\right)=\frac{3}{4}{x}^6-2x^4+\frac{5}{4}{x}^2+4-\frac{1}{4}{x}^6-2x^4-x^3+\frac{1}{4}{x}^2+2x-2=\frac{1}{2}{x}^6-4x^4-x^3+\frac{3}{2}{x}^2+2x+2$  

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$\text{b)}f\left(x\right)+g\left(x\right)=-2x^2+4x-x^6+2-5x+3x^2+x^6-3x^5=-3x^5+x^2-x+2$  

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$f\left(x\right)-g\left(x\right)=\left(-2x^2+4x-x^6+2\right)-\left(-5x+3x^2+x^6-3x^5\right)=-2x^2+4x-x^6+2+5x-3x^2-x^6+3x^5=-2x^6+3x^5-5x^2+9x+2$  

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$\text{c)}f\left(x\right)+g\left(x\right)=3x^4+2x^7-5+4x-3x+x^5-2x^7+2=x^5+3x^4+x-3$  

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$f\left(x\right)-g\left(x\right)=\left(3x^4+2x^7-5+4x\right)-\left(-3x+x^5-2x^7+2\right)=3x^4+2x^7-5+4x+3x-x^5+2x^7-2=4x^7-x^5+3x^4+7x-7$