What is the answer to (bx)/a-d/c = a/b-(cx)/d ?

The answer to (bx)/a-d/c = a/b-(cx)/d is x=(ad}{bc};\quad badc\ne 0,b\ne 0,b\ne-\frac{ac)/d

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(bx)/a-d/c = a/b-(cx)/d

\frac{b x}{a} - \frac{d}{c} = \frac{a}{b} - \frac{c x}{d}

x = \frac{a d}{b c}; ba d c \neq = 0, b \neq = 0, b \neq = - \frac{a c}{d}

Solution steps

\frac{b x}{a} - \frac{d}{c} = \frac{a}{b} - \frac{c x}{d}

Move

\frac{c x}{d}

to the left side

\frac{b x}{a} - \frac{d}{c} + \frac{c x}{d} = \frac{a}{b}

Multiply by LCM

b^{2} d c x - ba d^{2} + ba c^{2} x = a^{2} d c; ba d c \neq = 0

Move

ba d^{2}

to the right side

b^{2} d c x + ba c^{2} x = a^{2} d c + ba d^{2}; ba d c \neq = 0

Factor

b^{2} d c x + ba c^{2} x : b c x (b d + a c)

b c x (b d + a c) = a^{2} d c + ba d^{2}; ba d c \neq = 0

Divide both sides by

b c (b d + a c); ba d c \neq = 0, b \neq = 0, b \neq = - \frac{a c}{d}

x = \frac{a d}{b c}; ba d c \neq = 0, b \neq = 0, b \neq = - \frac{a c}{d}

a, a x^{3} + b x^{2} + c x + d = 0

- 2 (3 x + 4) = - 4 (x - 2) - 2 x

x, 2 x - 3 y - 5 z = - 19

9 = 9^{\frac{1}{2}}

2 \cdot (x - 2) = 60 - 3 \cdot (1 - x)

What is the answer to (bx)/a-d/c = a/b-(cx)/d ?
The answer to (bx)/a-d/c = a/b-(cx)/d is x=(ad}{bc};\quad badc\ne 0,b\ne 0,b\ne-\frac{ac)/d