Mister Exam
Expression simplification/
Least common denominator/
(((x-x1)*(x-x2))/((x0-x1)*(x0-x2)))*y0+(((x-x0)*(x-x2))/((x1-x0)*(x1-x2)))*y1
Least common denominator (((x-x1)*(x-x2))/((x0-x1)*(x0-x2)))*y0+(((x-x0)*(x-x2))/((x1-x0)*(x1-x2)))*y1
The solution
You have entered
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(x - x1)*(x - x2) (x - x0)*(x - x2) -------------------*y0 + -------------------*y1 (x0 - x1)*(x0 - x2) (x1 - x0)*(x1 - x2)
$$y_{0} \frac{\left(x - x_{1}\right) \left(x - x_{2}\right)}{\left(x_{0} - x_{1}\right) \left(x_{0} - x_{2}\right)} + y_{1} \frac{\left(x - x_{0}\right) \left(x - x_{2}\right)}{\left(- x_{0} + x_{1}\right) \left(x_{1} - x_{2}\right)}$$
(((x - x1)*(x - x2))/(((x0 - x1)*(x0 - x2))))*y0 + (((x - x0)*(x - x2))/(((x1 - x0)*(x1 - x2))))*y1
General simplification
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(x - x2)*(y0*(x - x1)*(x1 - x2) - y1*(x - x0)*(x0 - x2))
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(x0 - x1)*(x0 - x2)*(x1 - x2)
$$\frac{\left(x - x_{2}\right) \left(y_{0} \left(x - x_{1}\right) \left(x_{1} - x_{2}\right) - y_{1} \left(x - x_{0}\right) \left(x_{0} - x_{2}\right)\right)}{\left(x_{0} - x_{1}\right) \left(x_{0} - x_{2}\right) \left(x_{1} - x_{2}\right)}$$
(x - x2)*(y0*(x - x1)*(x1 - x2) - y1*(x - x0)*(x0 - x2))/((x0 - x1)*(x0 - x2)*(x1 - x2))
Numerical answer
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y0*(x - x1)*(x - x2)/((x0 - x1)*(x0 - x2)) + y1*(x - x0)*(x - x2)/((x1 - x0)*(x1 - x2))
y0*(x - x1)*(x - x2)/((x0 - x1)*(x0 - x2)) + y1*(x - x0)*(x - x2)/((x1 - x0)*(x1 - x2))
Rational denominator
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y0*(x - x1)*(x - x2)*(x1 - x0)*(x1 - x2) + y1*(x - x0)*(x - x2)*(x0 - x1)*(x0 - x2)
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(x0 - x1)*(x0 - x2)*(x1 - x0)*(x1 - x2)
$$\frac{y_{0} \left(x - x_{1}\right) \left(x - x_{2}\right) \left(- x_{0} + x_{1}\right) \left(x_{1} - x_{2}\right) + y_{1} \left(x - x_{0}\right) \left(x - x_{2}\right) \left(x_{0} - x_{1}\right) \left(x_{0} - x_{2}\right)}{\left(- x_{0} + x_{1}\right) \left(x_{0} - x_{1}\right) \left(x_{0} - x_{2}\right) \left(x_{1} - x_{2}\right)}$$
(y0*(x - x1)*(x - x2)*(x1 - x0)*(x1 - x2) + y1*(x - x0)*(x - x2)*(x0 - x1)*(x0 - x2))/((x0 - x1)*(x0 - x2)*(x1 - x0)*(x1 - x2))
Trigonometric part
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y0*(x - x1)*(x - x2) y1*(x - x0)*(x - x2) -------------------- + -------------------- (x0 - x1)*(x0 - x2) (x1 - x0)*(x1 - x2)
$$\frac{y_{0} \left(x - x_{1}\right) \left(x - x_{2}\right)}{\left(x_{0} - x_{1}\right) \left(x_{0} - x_{2}\right)} + \frac{y_{1} \left(x - x_{0}\right) \left(x - x_{2}\right)}{\left(- x_{0} + x_{1}\right) \left(x_{1} - x_{2}\right)}$$
y0*(x - x1)*(x - x2)/((x0 - x1)*(x0 - x2)) + y1*(x - x0)*(x - x2)/((x1 - x0)*(x1 - x2))
Common denominator
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/ 2 2 2 2 2 2 2 2 2 2 2 2\
-\x*y0*x1 + x*y1*x2 + x0*y1*x + x1*y0*x2 + x2*y0*x + x2*y1*x0 - x*y0*x2 - x*y1*x0 - x0*y1*x2 - x1*y0*x - x2*y0*x1 - x2*y1*x /
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2 2 2 2 2 2
x0*x2 + x1*x0 + x2*x1 - x0*x1 - x1*x2 - x2*x0
$$- \frac{x^{2} x_{0} y_{1} - x^{2} x_{1} y_{0} + x^{2} x_{2} y_{0} - x^{2} x_{2} y_{1} - x x_{0}^{2} y_{1} + x x_{1}^{2} y_{0} - x x_{2}^{2} y_{0} + x x_{2}^{2} y_{1} + x_{0}^{2} x_{2} y_{1} - x_{0} x_{2}^{2} y_{1} - x_{1}^{2} x_{2} y_{0} + x_{1} x_{2}^{2} y_{0}}{x_{0}^{2} x_{1} - x_{0}^{2} x_{2} - x_{0} x_{1}^{2} + x_{0} x_{2}^{2} + x_{1}^{2} x_{2} - x_{1} x_{2}^{2}}$$
-(x*y0*x1^2 + x*y1*x2^2 + x0*y1*x^2 + x1*y0*x2^2 + x2*y0*x^2 + x2*y1*x0^2 - x*y0*x2^2 - x*y1*x0^2 - x0*y1*x2^2 - x1*y0*x^2 - x2*y0*x1^2 - x2*y1*x^2)/(x0*x2^2 + x1*x0^2 + x2*x1^2 - x0*x1^2 - x1*x2^2 - x2*x0^2)
Combinatorics
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/ 2 2 \
-(x - x2)*\y0*x1 - y1*x0 + x*x0*y1 + x*x2*y0 + x0*x2*y1 - x*x1*y0 - x*x2*y1 - x1*x2*y0/
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(x0 - x1)*(x0 - x2)*(x1 - x2)
$$- \frac{\left(x - x_{2}\right) \left(x x_{0} y_{1} - x x_{1} y_{0} + x x_{2} y_{0} - x x_{2} y_{1} - x_{0}^{2} y_{1} + x_{0} x_{2} y_{1} + x_{1}^{2} y_{0} - x_{1} x_{2} y_{0}\right)}{\left(x_{0} - x_{1}\right) \left(x_{0} - x_{2}\right) \left(x_{1} - x_{2}\right)}$$
-(x - x2)*(y0*x1^2 - y1*x0^2 + x*x0*y1 + x*x2*y0 + x0*x2*y1 - x*x1*y0 - x*x2*y1 - x1*x2*y0)/((x0 - x1)*(x0 - x2)*(x1 - x2))
Powers
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y0*(x - x1)*(x - x2) y1*(x - x0)*(x - x2) -------------------- + -------------------- (x0 - x1)*(x0 - x2) (x1 - x0)*(x1 - x2)
$$\frac{y_{0} \left(x - x_{1}\right) \left(x - x_{2}\right)}{\left(x_{0} - x_{1}\right) \left(x_{0} - x_{2}\right)} + \frac{y_{1} \left(x - x_{0}\right) \left(x - x_{2}\right)}{\left(- x_{0} + x_{1}\right) \left(x_{1} - x_{2}\right)}$$
y0*(x - x1)*(x - x2)/((x0 - x1)*(x0 - x2)) + y1*(x - x0)*(x - x2)/((x1 - x0)*(x1 - x2))
Combining rational expressions
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(x - x2)*(y0*(x - x1)*(x1 - x0)*(x1 - x2) + y1*(x - x0)*(x0 - x1)*(x0 - x2))
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(x0 - x1)*(x0 - x2)*(x1 - x0)*(x1 - x2)
$$\frac{\left(x - x_{2}\right) \left(y_{0} \left(x - x_{1}\right) \left(- x_{0} + x_{1}\right) \left(x_{1} - x_{2}\right) + y_{1} \left(x - x_{0}\right) \left(x_{0} - x_{1}\right) \left(x_{0} - x_{2}\right)\right)}{\left(- x_{0} + x_{1}\right) \left(x_{0} - x_{1}\right) \left(x_{0} - x_{2}\right) \left(x_{1} - x_{2}\right)}$$
(x - x2)*(y0*(x - x1)*(x1 - x0)*(x1 - x2) + y1*(x - x0)*(x0 - x1)*(x0 - x2))/((x0 - x1)*(x0 - x2)*(x1 - x0)*(x1 - x2))
Assemble expression
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y0*(x - x1)*(x - x2) y1*(x - x0)*(x - x2) -------------------- + -------------------- (x0 - x1)*(x0 - x2) (x1 - x0)*(x1 - x2)
$$\frac{y_{0} \left(x - x_{1}\right) \left(x - x_{2}\right)}{\left(x_{0} - x_{1}\right) \left(x_{0} - x_{2}\right)} + \frac{y_{1} \left(x - x_{0}\right) \left(x - x_{2}\right)}{\left(- x_{0} + x_{1}\right) \left(x_{1} - x_{2}\right)}$$
y0*(x - x1)*(x - x2)/((x0 - x1)*(x0 - x2)) + y1*(x - x0)*(x - x2)/((x1 - x0)*(x1 - x2))