Question

Simplify the expression. State any excluded values.

x^ 2 - 36/42x - 7x^ 2

Answer 1

Consider the expression $x^2-\dfrac{36}{42}x-7x^2.$

This expression contains two terms with $x^2,$ group them:

$x^2-7x^2=x^2(1-7)=-6x^2.$

Now simplify term $\dfrac{36}{42}x=\dfrac{6}{7}x.$

Now $x^2-\dfrac{36}{42}x-7x^2=-6x^2-\dfrac{6}{7}x=6\left(-x^2-\dfrac{1}{7}x\right)=-6x\left(x-\dfrac{1}{7}\right).$

This expression is defined for all x.