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\frac{1}{4}-\frac{12}{4}+1+\sqrt{8}\times \frac{\sqrt{2}}{2}
Convert 3 to fraction \frac{12}{4}.
\frac{1-12}{4}+1+\sqrt{8}\times \frac{\sqrt{2}}{2}
Since \frac{1}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.
-\frac{11}{4}+1+\sqrt{8}\times \frac{\sqrt{2}}{2}
Subtract 12 from 1 to get -11.
-\frac{11}{4}+\frac{4}{4}+\sqrt{8}\times \frac{\sqrt{2}}{2}
Convert 1 to fraction \frac{4}{4}.
\frac{-11+4}{4}+\sqrt{8}\times \frac{\sqrt{2}}{2}
Since -\frac{11}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.
-\frac{7}{4}+\sqrt{8}\times \frac{\sqrt{2}}{2}
Add -11 and 4 to get -7.
-\frac{7}{4}+2\sqrt{2}\times \frac{\sqrt{2}}{2}
Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.
-\frac{7}{4}+\sqrt{2}\sqrt{2}
Cancel out 2 and 2.
-\frac{7}{4}+2
Multiply \sqrt{2} and \sqrt{2} to get 2.
-\frac{7}{4}+\frac{8}{4}
Convert 2 to fraction \frac{8}{4}.
\frac{-7+8}{4}
Since -\frac{7}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.
\frac{1}{4}
Add -7 and 8 to get 1.