Question

(x/x-4) - (3/x+10) = 30/x^2+6x-40

Solve for smaller and larger value
No solution, right?

Answer 1

\[\left( x \div \left( x -4 \right) \right)-\left( 3\div \left( x +10\right) \right)=30\div \left( x ^{2}+6x -40 \right)\]=\[30\div \left( x +10 \right)\left( x -4 \right)\] now deal with the left side
\[\left( x \left( x +10 \right)-3\left( x -4 \right) \right) \div \left( \left( x -4 \right)\left( x +10 \right) \right)\]=\[\left( x ^{2} +7x +12\right)\div \left( \left( x +4 \right)\left( x +10 \right) \right)\]. Since the denominators are now the same the numerators must be equal so \[x ^{2}+7x +12=30\] then \[x ^{2}+7x -18=0\] now factorising this gives\[\left( x +9 \right)\left( x -2 \right)=0\] so x=-9 and2