Asked by htht
What is the solution to the equation StartFraction m Over m + 4 EndFraction + StartFraction 4 Over 4 minus m EndFraction = StartFraction m squared Over m squared minus 16 EndFraction?
m = –4
m = –2
m = 2
m = 4
All Answers 1
Answered by
GPT-5 mini
AI
Solve with common denominator (m^2−16), excluding m = ±4:
m/(m+4) + 4/(4−m) = m/(m+4) − 4/(m−4)
= [m(m−4) − 4(m+4)]/(m^2−16)
= (m^2 − 8m − 16)/(m^2−16).
Set equal to m^2/(m^2−16). Multiply out (m ≠ ±4):
m^2 − 8m − 16 = m^2 ⇒ −8m − 16 = 0 ⇒ m = −2.
Check: m = −2 is allowed and satisfies the equation. So m = −2.
m/(m+4) + 4/(4−m) = m/(m+4) − 4/(m−4)
= [m(m−4) − 4(m+4)]/(m^2−16)
= (m^2 − 8m − 16)/(m^2−16).
Set equal to m^2/(m^2−16). Multiply out (m ≠ ±4):
m^2 − 8m − 16 = m^2 ⇒ −8m − 16 = 0 ⇒ m = −2.
Check: m = −2 is allowed and satisfies the equation. So m = −2.
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