Washington (CNN) With major Supreme Court decisions on health care and same-sex marriage expected this month, many lack trust in the Supreme Court's handling of those two issues, according to a new CNN/ORC poll.

Yet most approve of the way the court is handling its job generally.

A majority, 52%, say they approve of the way the court is handling its job, while 41% disapprove. That's an improvement from an even 48% to 48% split two years ago. Still, when Americans are asked how much they trust the court on a range of issues it will be considering this term or the next, the worst ratings come on health care and same-sex marriage. Only about half say they have at least a moderate amount of trust in the court on health care (50%) or same-sex marriage (49%). There is more faith in the Supreme Court on other key issues on the docket, with most saying they trust the court at least a moderate amount on freedom of speech (69%), voting rights (65%) and the death penalty (60%).

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The court's most recent rulings on same-sex marriage have tilted in favor of those who support legal marriages, a growing group among the American public. In this poll, 63% say they believe gay and lesbian couples have a constitutional right to marry. Only 49% said that was a constitutional right as recently as 2010.

The nearly two-thirds who currently say there is a constitutional right for same-sex couples to marry includes about three-quarters of Americans under age 50 (73%) and roughly half of those over age 50 (52%). Majorities of Democrats (74%) and independents (69%) see a constitutional right to marry for same-sex couples, while only 35% of Republicans agree. There is a significant age gap among Republicans and Republican-leaning independents, however, with 59% of those under age 50 saying same-sex couples do have a constitutional right to marry, compared with 36% of Republican-leaners age 50 or older.

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