The simplification of rational expression (x²+6x-7)/(x²+9x+14) gives
(x-1)/(x+2).
<h3>What is factorisation?</h3>
A polynomial or integer is simply resolved into components that, when multiplied together, produce the original or starting polynomial or integer.
- The factorization method allows us to simplify any algebraic and quadratic equation by representing the equations as that of the product or factors rather than by expanding the brackets.
- Any equation can have an integer, a variable, or the algebraic expression itself as a factor.
The given expression is -
= (x²+6x-7)/(x²+9x+14)
Factorising both numerator and denominator;
= {x+7x-x-7} / {x+7x+2x+14}
= {x(x+7)-(x+7)} / {x(x+7)+2(x+7)}
= {(x+7)(x-1)} / {(x+7)(x+2)}
Cancel the (x+7),
= (x-1)/(x+2)
Therefore, the simplification of the given equation is (x-1)/(x+2).
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