Question

which rational expression
should be subteracted from
7x/x^+x-12
to get
4/4+x
?​

Answer 1

$\frac{7x}{ {x}^{2} + x -12 } - y = \frac{4}{4 + x} \\ \frac{7x}{ {x}^{2} +4 x - 3x -12 } - y = \frac{4}{4 + x} \\ \frac{7x}{ x(x +4 ) - 3( x + 4) } - y = \frac{4}{4 + x} \\ \frac{7x}{ (x +4 )( x - 3) } - y = \frac{4}{4 + x} \\ \frac{4}{4 + x} \\ y = \frac{7x}{ (x +4 )( x - 3) } - \frac{4}{4 + x} \\ y = \frac{7x - 4(x - 3)}{(x + 4)(x - 3)} \\ y = \frac{7x - 4x - 12}{(x + 4)(x - 3)} \\ y = \frac{3x - 12}{(x + 4)(x - 3) } \\ y = \frac{(x - 4)}{(x + 4)(x - 3)}$

Rational expression

$\frac{(x - 4)}{(x + 4)(x - 3)}$

Should be subtracted from

$\frac{7x}{ {x}^{2} + x - 12}$

To get

$\frac{4}{4 + x}$