Solve for x
:
A = \dfrac{B}{expr(["*", C, "x"]) + D}
ANSWER
Multiply both sides by expr(["*", C, "x"]) + D
:
\qquad A (expr(["*", C, "x"]) + D) = \dfrac{B}{expr(["*", C, "x"]) + D} (expr(["*", C, "x"]) + D)
\qquad A * Cx + A * D = B
Now A * D < 0 ? "add" : "subtract" abs( A * D )
A * D < 0 ? "to" : "from" both sides:
\qquad (A * Cx + A * D) + -A * D = B + - A * D
\qquad A * Cx = B - A * D
Divide by A * C
:
\qquad x = fractionReduce( B - A * D, A * C )
Solve for x
:
\dfrac{expr(["*", A, "x"]) + B}{expr(["*", C, "x"]) + D} = E
ANSWER
Multiply both sides by expr(["*", C, "x"]) + D
:
\qquad \dfrac{expr(["*", A, "x"]) + B}{expr(["*", C, "x"]) + D} (expr(["*", C, "x"]) + D) = E (expr(["*", C, "x"]) + D)
\qquad expr(["*", A, "x"]) + B = expr(["*", E * C, "x"]) + E * D
Now E * C < 0 ? "add" : "subtract" abs( E * C )x
E * C < 0 ? "to" : "from" both sides:
\qquad (expr(["*", A, "x"]) + B) + -E * Cx = (expr(["*", E * C, "x"]) + E * D) + -E * Cx
\qquad A - E * Cx + B = E * D
Now B < 0 ? "add" : "subtract" abs( B )
:
\qquad (A - E * Cx + B) + -B = E * D + -B
\qquad A - E * Cx = E * D - B
Divide by A - E * C
:
\qquad x = fractionReduce( E * D - B, A - E * C )