Mister Exam
Expression simplification/
Fraction Decomposition into the simple/
((z+2)/(2*z+4))+((2*z+1)/(3*z-4))
How do you ((z+2)/(2*z+4))+((2*z+1)/(3*z-4)) in partial fractions?
The solution
You have entered
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z + 2 2*z + 1 ------- + ------- 2*z + 4 3*z - 4
$$\frac{z + 2}{2 z + 4} + \frac{2 z + 1}{3 z - 4}$$
(z + 2)/(2*z + 4) + (2*z + 1)/(3*z - 4)
Fraction decomposition
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7/6 + 11/(3*(-4 + 3*z))
$$\frac{7}{6} + \frac{11}{3 \left(3 z - 4\right)}$$
7 11 - + ------------ 6 3*(-4 + 3*z)
General simplification
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-2 + 7*z ------------ 2*(-4 + 3*z)
$$\frac{7 z - 2}{2 \left(3 z - 4\right)}$$
(-2 + 7*z)/(2*(-4 + 3*z))
Numerical answer
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(2.0 + z)/(4.0 + 2.0*z) + (1.0 + 2.0*z)/(-4.0 + 3.0*z)
(2.0 + z)/(4.0 + 2.0*z) + (1.0 + 2.0*z)/(-4.0 + 3.0*z)
Combining rational expressions
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-2 + 7*z ------------ 2*(-4 + 3*z)
$$\frac{7 z - 2}{2 \left(3 z - 4\right)}$$
(-2 + 7*z)/(2*(-4 + 3*z))
Combinatorics
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-2 + 7*z ------------ 2*(-4 + 3*z)
$$\frac{7 z - 2}{2 \left(3 z - 4\right)}$$
(-2 + 7*z)/(2*(-4 + 3*z))
Common denominator
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7 11 - + --------- 6 -12 + 9*z
$$\frac{7}{6} + \frac{11}{9 z - 12}$$
7/6 + 11/(-12 + 9*z)
Rational denominator
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(1 + 2*z)*(4 + 2*z) + (-4 + 3*z)*(2 + z)
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(-4 + 3*z)*(4 + 2*z)
$$\frac{\left(z + 2\right) \left(3 z - 4\right) + \left(2 z + 1\right) \left(2 z + 4\right)}{\left(2 z + 4\right) \left(3 z - 4\right)}$$
((1 + 2*z)*(4 + 2*z) + (-4 + 3*z)*(2 + z))/((-4 + 3*z)*(4 + 2*z))