Solve for x (complex solution)
x\in \mathrm{C}\setminus -\frac{4}{5},\frac{4}{5}
Solve for x
x\in \mathrm{R}\setminus -\frac{4}{5},\frac{4}{5}
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\left(5x-4\right)\times 2+\left(5x+4\right)\times 3=25x+4
Variable x cannot be equal to any of the values -\frac{4}{5},\frac{4}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5x-4\right)\left(5x+4\right), the least common multiple of 5x+4,5x-4,25x^{2}-16.
10x-8+\left(5x+4\right)\times 3=25x+4
Use the distributive property to multiply 5x-4 by 2.
10x-8+15x+12=25x+4
Use the distributive property to multiply 5x+4 by 3.
25x-8+12=25x+4
Combine 10x and 15x to get 25x.
25x+4=25x+4
Add -8 and 12 to get 4.
25x+4-25x=4
Subtract 25x from both sides.
4=4
Combine 25x and -25x to get 0.
\text{true}
Compare 4 and 4.
x\in \mathrm{C}
This is true for any x.
x\in \mathrm{C}\setminus -\frac{4}{5},\frac{4}{5}
Variable x cannot be equal to any of the values -\frac{4}{5},\frac{4}{5}.
\left(5x-4\right)\times 2+\left(5x+4\right)\times 3=25x+4
Variable x cannot be equal to any of the values -\frac{4}{5},\frac{4}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5x-4\right)\left(5x+4\right), the least common multiple of 5x+4,5x-4,25x^{2}-16.
10x-8+\left(5x+4\right)\times 3=25x+4
Use the distributive property to multiply 5x-4 by 2.
10x-8+15x+12=25x+4
Use the distributive property to multiply 5x+4 by 3.
25x-8+12=25x+4
Combine 10x and 15x to get 25x.
25x+4=25x+4
Add -8 and 12 to get 4.
25x+4-25x=4
Subtract 25x from both sides.
4=4
Combine 25x and -25x to get 0.
\text{true}
Compare 4 and 4.
x\in \mathrm{R}
This is true for any x.
x\in \mathrm{R}\setminus -\frac{4}{5},\frac{4}{5}
Variable x cannot be equal to any of the values -\frac{4}{5},\frac{4}{5}.
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