How do you simplify #x/(x-8) - 2/(x+7)#?

Question

Julia Adams · Accepted Answer

#[x^2+5x+16]/[x^2-x-56]# #x/(x-8) - 2/(x+7)# Cross multiply to get a common denominator #[x(x+7)-2(x-8)]/{(x-8)(x+7)]# #[x^2+7x-2x+16]/[x^2+7x-8x-56]# #[x^2+5x+16]/[x^2-x-56]#

Hazel Anglin · Answer

#color(brown)(x^2 + 5x + 16 = 0# #x / (x - 8) = 2 / (x + 7)# #x *(x + 7) = 2*(x - 8)#, cross multiplying #x^2 + 7x = 2x - 16#, removing braces #x^2 + 7x -2x + 16 = 0# #x^2 + 5x + 16 = 0#

Eva Abramson · Answer

undefined To simplify the expression x/(x-8) - 2/(x+7), you need to find a common denominator for the two fractions. The common denominator is (x-8)(x+7).

Next, multiply the numerator and denominator of the first fraction, x/(x-8), by (x+7). This gives you (x(x+7))/((x-8)(x+7)).

Similarly, multiply the numerator and denominator of the second fraction, 2/(x+7), by (x-8). This gives you (2(x-8))/((x-8)(x+7)).

Now, you can combine the two fractions by subtracting the second fraction from the first fraction:

(x(x+7))/((x-8)(x+7)) - (2(x-8))/((x-8)(x+7)).

To simplify further, you can combine the numerators over the common denominator:

(x(x+7) - 2(x-8))/((x-8)(x+7)).

Expanding the numerator gives you:

(x^2 + 7x - 2x + 16)/((x-8)(x+7)).

Combining like terms in the numerator:

(x^2 + 5x + 16)/((x-8)(x+7)).

Therefore, the simplified expression is (x^2 + 5x + 16)/((x-8)(x+7)).