TS EAPCET (Engineering) Partial Fraction Decomposition — practice questions
42 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAPCET (Engineering) Partial Fraction Decomposition in the app →If (3x+5)/((x+1)(x+2)) = A/(x+1) + B/(x+2), find A.Resolving 1/((x-1)(x-2)) into partial fractions, the numerator over (x-1) isSplit x/((x-1)(x-2)) into two terms; the numerator over (x-2) isExpress (x+7)/((x+1)(x+3)) as P/(x+1) + Q/(x+3); then P + Q isDecompose 1/(x²-1); the numerator beside (x-1) turns out to beThe coefficient of 1/(x+a) in the decomposition of 1/(x²-a²) isBreak up 1/(x²-4) into linear parts. The constant over (x-2) isConstants A and B satisfy (5x+1)/((x-1)(x+2)) = A/(x-1) + B/(x+2). Their product isWhat must be done first to decompose (x³+1)/(x²-1)?The correct form of 1/((x-1)(x²+1)) isHow many unknown constants does the form of x/(x-1)³ have?For (x²+1)/((x-1)(x+2)(x²+x+1)), how many constants are needed in the form?Which quadratic cannot be factorised over the real numbers?Given (3x+5)/(1-2x)² = A/(1-2x)² + B/(1-2x), determine the constant A.Splitting 1/(x²(x+1)) into A/x, B/x² and C/(x+1) terms, A must beWhat numerator sits above (x+1) when 1/((x-1)²(x+1)) is split up?The polynomial part of x²/(x²-1) isDividing x³ by x²-1 gives a quotient ofFind the constant above (x+1) when 1/((x+1)(x²+1)) is split into partial fractions.After splitting 1/((x+1)(x²+1)), the coefficient of x in the quadratic's numerator isUsing the cover-up rule on 1/((x-1)(x-3)), the numerator beside (x-3) isWhich numerator accompanies (x+3) when 5/((x-2)(x+3)) is split?The definite integral of dx/(x²-1) from x = 2 to 3 isFor a given rational fraction, how many decompositions of the standard form exist?Over the complex numbers, every irreducible polynomial has degreeUsing the primes 2 and 3 as denominators, 1/6 can be written asHow many partial fractions are there in 1/((x-1)(x-2)(x-3))?In 1/((x-1)(x-2)(x-3)), the constant over (x-2) isFor 1/((x-1)(x-2)(x-3)), the three constants A, B, C add up toDecompose (x²+x+1)/(x(x²+1)) into partial fractions.For x/(x²+3x+2), the numerator over (x+2) in its partial fractions isThe limit of x times (x+3)/(x(x+1)(x+2)) as x tends to 0 gives the coefficient of 1/x asFind A + B when 1/((x+1)(x+2)) is written as A/(x+1) + B/(x+2).For (x²+1)/(x(x-1)(x+1)) with constants A, B, C, the sum A + B + C isHow many terms are in the form of 1/(x²(x-1)²)?Determine B after splitting (x+2)/(x-1)² into A/(x-1) and B/(x-1)².Rewrite 1/(x²-5x+6) as a difference of two simple fractions.The sum of 1/(n(n+1)) for n = 1 to 9 equalsA rational fraction P/Q is called proper whenPartial fraction decomposition writes a fraction as a polynomial plusThe numerator over an irreducible quadratic factor must have degreeNumerator above (x-1) in the partial fractions of 3/((x-1)(x+2))?