Solve for: 414 Request-URI Too Large

Expression: $\frac{ 5 }{ a }+\frac{ 7 }{ 2 }=-\frac{ 7 }{ 5 }+\frac{ 3 }{ 2a }$

Determine the defined range

$\begin{array} { l }\frac{ 5 }{ a }+\frac{ 7 }{ 2 }=-\frac{ 7 }{ 5 }+\frac{ 3 }{ 2a },& a≠0\end{array}$

Move the expression to the left-hand side and change its sign

$\frac{ 5 }{ a }+\frac{ 7 }{ 2 }-\frac{ 3 }{ 2a }=-\frac{ 7 }{ 5 }$

Move the constant to the right-hand side and change its sign

$\frac{ 5 }{ a }-\frac{ 3 }{ 2a }=-\frac{ 7 }{ 5 }-\frac{ 7 }{ 2 }$

Write all numerators above the least common denominator $2a$

$\frac{ 7 }{ 2a }=-\frac{ 7 }{ 5 }-\frac{ 7 }{ 2 }$

Calculate the difference

$\frac{ 7 }{ 2a }=-\frac{ 49 }{ 10 }$

Simplify the equation using cross-multiplication

$70=-98a$

Swap the sides of the equation

$-98a=70$

Divide both sides of the equation by $-98$

$\begin{array} { l }a=-\frac{ 5 }{ 7 },& a≠0\end{array}$

Check if the solution is in the defined range

$\begin{align*}&a=-\frac{ 5 }{ 7 } \\&a=-0.\overset{ \cdot }{ 7 } 1428\overset{ \cdot }{ 5 } \end{align*}$