Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
-$$\frac { 6 } { y + 5 } - \frac { 9 } { y - 5 } = \frac { 12 } { y ^ { 2 } - 25 }$$
A) Identity
B) Conditional equation
C) Inconsistent equation

Question

Quizplus · Accepted Answer

This is a conditional equation because it is true for specific values of $y$. The equation simplifies to an equivalent form when considering that $y^2 - 25$ is the common denominator, which is a difference of squares and factors into $(y + 5)(y - 5)$. The equation is not true for all values of $y$ (for example, it's undefined for $y = 5$ and $y = -5$), nor is it inconsistent (which would mean no solution).

Determine Whether the Equation Is an Identity, a Conditional Equation 6y+5−9y−5=12y2−25\frac { 6 } { y + 5 } - \frac { 9 } { y - 5 } = \frac { 12 } { y ^ { 2 } - 25 }y+56​−y−59​=y2−2512​

Determine Whether the Equation Is an Identity, a Conditional Equation $\frac { 6 } { y + 5 } - \frac { 9 } { y - 5 } = \frac { 12 } { y ^ { 2 } - 25 }$