Descomposición de una fracción
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sqrt(r^8/(r^8 + x^8 + 22*r^2*x^6 + 22*r^6*x^2 + 123*r^4*x^4) + r^4*x^4/(r^8 + x^8 + 22*r^2*x^6 + 22*r^6*x^2 + 123*r^4*x^4) + 11*r^6*x^2/(r^8 + x^8 + 22*r^2*x^6 + 22*r^6*x^2 + 123*r^4*x^4))
$$\sqrt{\frac{r^{8}}{r^{8} + 22 r^{6} x^{2} + 123 r^{4} x^{4} + 22 r^{2} x^{6} + x^{8}} + \frac{11 r^{6} x^{2}}{r^{8} + 22 r^{6} x^{2} + 123 r^{4} x^{4} + 22 r^{2} x^{6} + x^{8}} + \frac{r^{4} x^{4}}{r^{8} + 22 r^{6} x^{2} + 123 r^{4} x^{4} + 22 r^{2} x^{6} + x^{8}}}$$
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/ 8 4 4 6 2
/ r r *x 11*r *x
/ ----------------------------------------- + ----------------------------------------- + -----------------------------------------
/ 8 8 2 6 6 2 4 4 8 8 2 6 6 2 4 4 8 8 2 6 6 2 4 4
\/ r + x + 22*r *x + 22*r *x + 123*r *x r + x + 22*r *x + 22*r *x + 123*r *x r + x + 22*r *x + 22*r *x + 123*r *x
Simplificación general
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/ 4
/ r
/ ------------------
/ 4 4 2 2
\/ r + x + 11*r *x
$$\sqrt{\frac{r^{4}}{r^{4} + 11 r^{2} x^{2} + x^{4}}}$$
sqrt(r^4/(r^4 + x^4 + 11*r^2*x^2))
0.333333333333333*(r^6*x^2/(0.111111111111111*(r^2 + x^2)^2 + r^2*x^2)^2 + 0.111111111111111*r^4*(r^2 + x^2)^2/(0.111111111111111*(r^2 + x^2)^2 + r^2*x^2)^2)^0.5
0.333333333333333*(r^6*x^2/(0.111111111111111*(r^2 + x^2)^2 + r^2*x^2)^2 + 0.111111111111111*r^4*(r^2 + x^2)^2/(0.111111111111111*(r^2 + x^2)^2 + r^2*x^2)^2)^0.5
____________________
/ 4
/ r
/ ------------------
/ 4 4 2 2
\/ r + x + 11*r *x
$$\sqrt{\frac{r^{4}}{r^{4} + 11 r^{2} x^{2} + x^{4}}}$$
sqrt(r^4/(r^4 + x^4 + 11*r^2*x^2))
Parte trigonométrica
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/ 2
/ 4 / 2 2\ 6 2
/ r *\r + x / 9*r *x
/ ----------------------- + -----------------------
/ 2 2
/ / 2 \ / 2 \
/ |/ 2 2\ 2 2| |/ 2 2\ 2 2|
\/ \\r + x / + 9*r *x / \\r + x / + 9*r *x /
$$\sqrt{\frac{9 r^{6} x^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}} + \frac{r^{4} \left(r^{2} + x^{2}\right)^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}}}$$
sqrt(r^4*(r^2 + x^2)^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2 + 9*r^6*x^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2)
Compilar la expresión
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/ 2
/ 4 / 2 2\ 6 2
/ r *\r + x / 9*r *x
/ ----------------------- + -----------------------
/ 2 2
/ / 2 \ / 2 \
/ |/ 2 2\ 2 2| |/ 2 2\ 2 2|
\/ \\r + x / + 9*r *x / \\r + x / + 9*r *x /
$$\sqrt{\frac{9 r^{6} x^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}} + \frac{r^{4} \left(r^{2} + x^{2}\right)^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}}}$$
sqrt(r^4*(r^2 + x^2)^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2 + 9*r^6*x^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2)
____________________
/ 4
/ r
/ ------------------
/ 4 4 2 2
\/ r + x + 11*r *x
$$\sqrt{\frac{r^{4}}{r^{4} + 11 r^{2} x^{2} + x^{4}}}$$
sqrt(r^4/(r^4 + x^4 + 11*r^2*x^2))
Denominador racional
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/ / 2 \
/ 4 |/ 2 2\ 2 2|
/ r *\\r + x / + 9*r *x /
/ -------------------------------
/ 2
/ / 4 4 2 2 2\
\/ \r + x + (3*r*x) + 2*r *x /
$$\sqrt{\frac{r^{4} \left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)}{\left(r^{4} + 2 r^{2} x^{2} + x^{4} + \left(3 r x\right)^{2}\right)^{2}}}$$
sqrt(r^4*((r^2 + x^2)^2 + 9*r^2*x^2)/(r^4 + x^4 + ((3*r)*x)^2 + 2*r^2*x^2)^2)
Abrimos la expresión
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/ 4 2 6 2
/ r *(r*r + x*x) 9*r *x
/ ------------------------- + -------------------------
/ 2 2
/ / 2 2 2\ / 2 2 2\
\/ \(r*r + x*x) + x *9*r / \(r*r + x*x) + x *9*r /
$$\sqrt{\frac{9 r^{6} x^{2}}{\left(9 r^{2} x^{2} + \left(r r + x x\right)^{2}\right)^{2}} + \frac{r^{4} \left(r r + x x\right)^{2}}{\left(9 r^{2} x^{2} + \left(r r + x x\right)^{2}\right)^{2}}}$$
sqrt(r^4*(r*r + x*x)^2/((r*r + x*x)^2 + x^2*(9*r^2))^2 + 9*r^6*x^2/((r*r + x*x)^2 + x^2*(9*r^2))^2)
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/ 2
/ 4 / 2 2\ 6 2
/ r *\r + x / 9*r *x
/ ----------------------- + -----------------------
/ 2 2
/ / 2 \ / 2 \
/ |/ 2 2\ 2 2| |/ 2 2\ 2 2|
\/ \\r + x / + 9*r *x / \\r + x / + 9*r *x /
$$\sqrt{\frac{9 r^{6} x^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}} + \frac{r^{4} \left(r^{2} + x^{2}\right)^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}}}$$
sqrt(r^4*(r^2 + x^2)^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2 + 9*r^6*x^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2)
Unión de expresiones racionales
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/ 4
/ r
/ --------------------
/ 2
/ / 2 2\ 2 2
\/ \r + x / + 9*r *x
$$\sqrt{\frac{r^{4}}{9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}}}$$
sqrt(r^4/((r^2 + x^2)^2 + 9*r^2*x^2))