Mister Exam
Expression simplification/
Least common denominator/
(x/4+7/16)*(x^4-3*x^2+5*x-3)+(x^3+x-2)*((-x^2)/4-7*x/16+1)
Least common denominator (x/4+7/16)*(x^4-3*x^2+5*x-3)+(x^3+x-2)*((-x^2)/4-7*x/16+1)
The solution
You have entered
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/ 2 \ /x 7 \ / 4 2 \ / 3 \ |-x 7*x | |- + --|*\x - 3*x + 5*x - 3/ + \x + x - 2/*|---- - --- + 1| \4 16/ \ 4 16 /
$$\left(\frac{x}{4} + \frac{7}{16}\right) \left(\left(5 x + \left(x^{4} - 3 x^{2}\right)\right) - 3\right) + \left(\left(x^{3} + x\right) - 2\right) \left(\left(- \frac{7 x}{16} + \frac{\left(-1\right) x^{2}}{4}\right) + 1\right)$$
(x/4 + 7/16)*(x^4 - 3*x^2 + 5*x - 3) + (x^3 + x - 2)*((-x^2)/4 - 7*x/16 + 1)
Fraction decomposition
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-53/16 + 53*x/16
$$\frac{53 x}{16} - \frac{53}{16}$$
53 53*x - -- + ---- 16 16
General simplification
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53 53*x - -- + ---- 16 16
$$\frac{53 x}{16} - \frac{53}{16}$$
-53/16 + 53*x/16
Common denominator
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53 53*x - -- + ---- 16 16
$$\frac{53 x}{16} - \frac{53}{16}$$
-53/16 + 53*x/16
Combining rational expressions
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/ / / 2\\\ / / 2\\
\-3 + x*\5 + x*\-3 + x ///*(7 + 4*x) + \-2 + x*\1 + x //*(16 + x*(-7 - 4*x))
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16
$$\frac{\left(4 x + 7\right) \left(x \left(x \left(x^{2} - 3\right) + 5\right) - 3\right) + \left(x \left(- 4 x - 7\right) + 16\right) \left(x \left(x^{2} + 1\right) - 2\right)}{16}$$
((-3 + x*(5 + x*(-3 + x^2)))*(7 + 4*x) + (-2 + x*(1 + x^2))*(16 + x*(-7 - 4*x)))/16
Rational denominator
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/ 4 2 \ / 3\ / 2\
(28 + 16*x)*\-3 + x - 3*x + 5*x/ + \-2 + x + x /*\64 - 28*x - 16*x /
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64
$$\frac{\left(16 x + 28\right) \left(x^{4} - 3 x^{2} + 5 x - 3\right) + \left(- 16 x^{2} - 28 x + 64\right) \left(x^{3} + x - 2\right)}{64}$$
((28 + 16*x)*(-3 + x^4 - 3*x^2 + 5*x) + (-2 + x + x^3)*(64 - 28*x - 16*x^2))/64
Trigonometric part
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/ 2\ /7 x\ / 4 2 \ | 7*x x | / 3\ |-- + -|*\-3 + x - 3*x + 5*x/ + |1 - --- - --|*\-2 + x + x / \16 4/ \ 16 4 /
$$\left(\frac{x}{4} + \frac{7}{16}\right) \left(x^{4} - 3 x^{2} + 5 x - 3\right) + \left(- \frac{x^{2}}{4} - \frac{7 x}{16} + 1\right) \left(x^{3} + x - 2\right)$$
(7/16 + x/4)*(-3 + x^4 - 3*x^2 + 5*x) + (1 - 7*x/16 - x^2/4)*(-2 + x + x^3)
Assemble expression
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/ 2\ /7 x\ / 4 2 \ | 7*x x | / 3\ |-- + -|*\-3 + x - 3*x + 5*x/ + |1 - --- - --|*\-2 + x + x / \16 4/ \ 16 4 /
$$\left(\frac{x}{4} + \frac{7}{16}\right) \left(x^{4} - 3 x^{2} + 5 x - 3\right) + \left(- \frac{x^{2}}{4} - \frac{7 x}{16} + 1\right) \left(x^{3} + x - 2\right)$$
(7/16 + x/4)*(-3 + x^4 - 3*x^2 + 5*x) + (1 - 7*x/16 - x^2/4)*(-2 + x + x^3)
Numerical answer
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(0.4375 + 0.25*x)*(-3.0 + x^4 + 5.0*x - 3.0*x^2) + (1.0 - 0.25*x^2 - 0.4375*x)*(-2.0 + x + x^3)
(0.4375 + 0.25*x)*(-3.0 + x^4 + 5.0*x - 3.0*x^2) + (1.0 - 0.25*x^2 - 0.4375*x)*(-2.0 + x + x^3)
Powers
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/ 2\ /7 x\ / 4 2 \ | 7*x x | / 3\ |-- + -|*\-3 + x - 3*x + 5*x/ + |1 - --- - --|*\-2 + x + x / \16 4/ \ 16 4 /
$$\left(\frac{x}{4} + \frac{7}{16}\right) \left(x^{4} - 3 x^{2} + 5 x - 3\right) + \left(- \frac{x^{2}}{4} - \frac{7 x}{16} + 1\right) \left(x^{3} + x - 2\right)$$
(7/16 + x/4)*(-3 + x^4 - 3*x^2 + 5*x) + (1 - 7*x/16 - x^2/4)*(-2 + x + x^3)