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\frac{41z-23}{35}
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\frac{41z-23}{35}
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\frac{7\times 4\left(2z-1\right)}{35}-\frac{5\times 3\left(z+2\right)}{35}+1
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 7 is 35. Multiply \frac{4\left(2z-1\right)}{5} times \frac{7}{7}. Multiply \frac{3\left(z+2\right)}{7} times \frac{5}{5}.
\frac{7\times 4\left(2z-1\right)-5\times 3\left(z+2\right)}{35}+1
Since \frac{7\times 4\left(2z-1\right)}{35} and \frac{5\times 3\left(z+2\right)}{35} have the same denominator, subtract them by subtracting their numerators.
\frac{56z-28-15z-30}{35}+1
Do the multiplications in 7\times 4\left(2z-1\right)-5\times 3\left(z+2\right).
\frac{41z-58}{35}+1
Combine like terms in 56z-28-15z-30.
\frac{41z-58}{35}+\frac{35}{35}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{35}{35}.
\frac{41z-58+35}{35}
Since \frac{41z-58}{35} and \frac{35}{35} have the same denominator, add them by adding their numerators.
\frac{41z-23}{35}
Combine like terms in 41z-58+35.
\frac{7\times 4\left(2z-1\right)}{35}-\frac{5\times 3\left(z+2\right)}{35}+1
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 7 is 35. Multiply \frac{4\left(2z-1\right)}{5} times \frac{7}{7}. Multiply \frac{3\left(z+2\right)}{7} times \frac{5}{5}.
\frac{7\times 4\left(2z-1\right)-5\times 3\left(z+2\right)}{35}+1
Since \frac{7\times 4\left(2z-1\right)}{35} and \frac{5\times 3\left(z+2\right)}{35} have the same denominator, subtract them by subtracting their numerators.
\frac{56z-28-15z-30}{35}+1
Do the multiplications in 7\times 4\left(2z-1\right)-5\times 3\left(z+2\right).
\frac{41z-58}{35}+1
Combine like terms in 56z-28-15z-30.
\frac{41z-58}{35}+\frac{35}{35}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{35}{35}.
\frac{41z-58+35}{35}
Since \frac{41z-58}{35} and \frac{35}{35} have the same denominator, add them by adding their numerators.
\frac{41z-23}{35}
Combine like terms in 41z-58+35.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}